Publications – Boris Andreianov

Submitted works

B. Andreianov, T. Girard. Existence of solutions to a class of one-dimensional models for pedestrian evacuations, in revision at SIAM J. Math. Anal.
Available as preprint HAL https://hal.science.fr/hal-03937464
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B. Andreianov, S.S. Ghoshal and K. Koumatos. Lack of controllability of the viscous Burgers equation. Part II: The L^2 setting, with a detour into the well-posedness of unbounded entropy solutions to scalar conservation laws, preprint. Available at hal.archives-ouvertes.fr/03680108
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Recent works / works to appear

(2023) B. Andreianov, M.D. Rosini and G. Stivaletta. On existence, stability and many-particle approximation of solutions of 1D Hughes model with linear costs. J. Differ. Equ., 369 (2023), pp. 253-298. DOI : https://doi.org/10.1016/j.jde.2023.06.004
Available as preprint HAL https://hal.archives-ouvertes.fr/hal-03289551
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(2023) B. Andreianov, A. Sylla. Finite volume approximation and well-posedness of conservation laws with moving interfaces under abstract coupling conditions, NoDEA Nonlinear Differ. Equ. Appl. vol.30, paper 53 (2023), pp. 1-33. DOI : https://doi.org/10.1007/s00030-023-00857-9
Available as preprint HAL https://hal.science/hal-03873169
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(2023) B. Andreianov, E.H. Quenjel. Nodal Discrete Duality numerical scheme for nonlinear diffusion problems on general meshes, IMA J. Numer. Anal., accepted. DOI : https://doi.org/10.1093/imanum/drad041
Available as preprint HAL https://hal.archives-ouvertes.fr/hal-03739675
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(2023) D. Amadori, B. Andreianov, M. Di Francesco, S. Fagioli, T. Girard, P. Goatin, P. Markowich, J.-F. Pietschmann, M.D. Rosini, G. Russo, G. Stivaletta and M.T. Wolfram. The mathematical theory of Hughes’ model: a survey of results, accepted in Crowd Dynamics, Volume 4 (N. Bellomo, L. Gibelli eds.), Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, to appear. Available as preprint HAL hal.archives-ouvertes.fr/04087181
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(2022) B. Andreianov, S.S. Ghoshal and K. Koumatos. Lack of controllability of the viscous Burgers equation: part I — the L^∞ setting, Journal of Evolution Equations, 22, 70 (2022), pp. 1-24. DOI : 10.1007/s00028-022-00831-5
Available as a Springer Nature SharedIt version https://rdcu.be/cTvKI and as preprint HAL hal.archives-ouvertes.fr/hal-02497181v3
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(2022) B. Andreianov and E.H. Quenjel. On numerical approximation of diffusion problems governed by variable-exponent nonlinear elliptic operators, Vietnam Journal of Mathematics, special issue in honor of A. Quarteroni’s 70th anniversary, 51 (2023), pp.213–243. DOI : 10.1007/s10013-022-00592-1 . Available as a Springer Nature SharedIt version https://rdcu.be/cYcIi and preprint HAL https://hal.archives-ouvertes.fr/hal-03644203
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(2022) B. Andreianov, A. Sylla. Existence analysis and numerical approximation for a second order model of traffic with orderliness marker, M3AS Math. Methods Models Appl. Sci., 32(7 )(2022), pp. 1295–1348, DOI : 10.1142/S0218202522500294 .
Available as preprint HAL https://hal.archives-ouvertes.fr/hal-03214129
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(2021) B. Andreianov, C. Donadello and M.D. Rosini. Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow, NoDEA Nonlinear Differ. Equ. Appl., 28(3) (2021), pp. 1-37. DOI : 10.1007/s00030-021-00689-5
Available as preprint HAL https://hal.archives-ouvertes.fr/hal-02877276
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(2020) N. Alibaud, B. Andreianov and A. Ouédraogo. Nonlocal dissipation measure and L1 kinetic theory for fractional conservation laws, Communications in PDEs, 45(9) (2020), pp.1213-1251, DOI: 10.1080/03605302.2020.1768542
Available as preprint HAL hal.archives-ouvertes.fr/hal-02320423
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(2020) B. Andreianov and A. Sylla. A macroscopic model to reproduce self-organization at bottlenecks, in R. Klöfkorn et al. (eds) Finite Volumes for Complex Applications IX – Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham, pp. 243-254, DOI: 10.1007/978-3-030-43651-3_21
Available as preprint HAL hal.archives-ouvertes.fr/hal-02526538
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(2020) B. Andreianov and M. Maliki. On classes of well-posedness for quasilinear diffusion equations in the whole space, Discrete Cont. Dyn. Syst. ser. S, special issue in honor of 70th birthday of Prof. Michel Pierre, 14(2) (2021) pp.505-531, DOI: 10.3934/dcdss.2020361
Available as preprint HAL hal.archives-ouvertes.fr/hal-02328003
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(2020) B. Andreianov and M. Brassart. Uniqueness of entropy solutions to fractional conservation laws with “fully infinite” speed of propagation, to appear in J. Differ. Equ. 268(2020), pp. 3903–3935 DOI:10.1016/j.jde.2019.10.008 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-02190753
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(2020) B. Andreianov and M.D. Rosini. Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic, in J. Banasiak et al.(eds) Semigroups of Operators – Theory and Applications. SOTA 2018. Springer Proceedings in Mathematics & Statistics, vol 325. Springer, Cham, 2020, pp. 113-135, DOI: 10.1007/978-3-030-46079-2_7
Available as preprint HAL hal.archives-ouvertes.fr/hal-02197482
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(2018) B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini. Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux. J. Math. Pures Appl., 116(2018), pp.309—346, DOI : 10.1016/j.matpur.2018.01.005 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01418272
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(2018) B. Andreianov, C. Donadello, U. Razafison and M.D Rosini. One-dimensional conservation laws with non-local point constraints on the flux. In : Crowd Dynamics, Volume 1 – Theory, Models, and Safety Problems (N. Bellomo, L. Gibelli eds.), Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, 2018, pp.103-135. DOI : 10.1007/978-3-030-05129 7_5
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(2017) B. Andreianov, C. Cancès and A. Moussa. A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs. J. Funct. Anal. 273(12) (2017), pp. 3633-3670, DOI : 10.1016/j.jfa.2017.08.010 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01142499
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(2017) B. Andreianov, G.M. Coclite and C. Donadello. Well-posedness for vanishing viscosity solutions of scalar conservation law on a network. Discrete Cont. Dyn. Syst. ser. A 37(11) (2017), pp. 5913-5942, DOI : 10.3934/dcds.2017257 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01312742
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(2017) B. Andreianov, C. Donadello and A. Marson. On the attainable set for a scalar nonconvex conservation law. SIAM J. Control Opt., 55(4) (2017), pp. 2235-2270, DOI : 10.1137/16M1085966 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01346993
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(2017) B. Andreianov, M. Kramar Fijavž, A. Peperko and E. Sikolya. Erratum to : Semigroups of max-plus linear operators. Semigroup Forum 94 (2017), no.2, pp 477-479, DOI : 10.1007/s00233-017-9870-9 .
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(2016) B. Andreianov, C. Donadello and M.D. Rosini. A second order model for vehicular traffics with local point constraints on the flow. M3AS Math. Methods Models Appl. Sci. 26(4) (2016), pp. 751—802, DOI : 10.1142/S0218202516500172 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01146116
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(2016) B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini. Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks. M2AN Math. Modelling and Numerical Analysis 50 (2016), pp. 1269-1287, DOI : 10.1051/m2an/2015078 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01121965
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(2016) B. Andreianov and M. Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolic-hyperbolic conservation laws. Netw. Heter. Media 11 (2) (2016), pp. 203-222 (special issue Contemporary Topics in Conservation Laws), DOI:10.3934/nhm.2016.11.203 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01152481
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(2016) B. Andreianov, C. Donadello, U. Razafison, J.-Y. Rolland and M. D. Rosini. Solutions of the Aw-Rascle-Zhang system with point constraints. Netw. Heter. Media 11 (1) (2016), pp. 29-47 (special issue Contemporary Topics in Conservation Laws), DOI : 10.3934/nhm.2016.11.29 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01191596
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(2015) B. Andreianov. New approaches to describing admissibility of solutions of scalar conservation laws with discontinuous flux. ESAIM : Proc. and Surveys 50 (2015), pp.40-65, DOI : dx.doi.org/10.1051/proc/201550003 .
Available as preprint HAL hal.archives-ouvertes.fr/hal-01109040
Cf. the related Beamer presentation at ICJ Lyon 2019
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Works of 1997 – 2015

(2015) B. Andreianov and C. Cancès. On interface transmission conditions for conservation laws with discontinuous flux of general shape. J. Hyperbolic Differ. Equ. 12 (2) (2015), pp. 343-384, DOI : 10.1142/S0219891615500101 .
Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00940756
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(2015) B. Andreianov, C. Donadello, S. S. Ghoshal and U. Razafison. On the attainable set for a class of triangular systems of conservation laws. J. Evol. Equ., . 15(3) (2015), pp. 503-532. DOI : 10.1007/s00028-014-0267-x .
Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00967600
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(2015) B. Andreianov and K. Sbihi. Well-posedness of general boundary-value problems for scalar conservation laws. Transactions AMS 367 (6) (2015), pp.3763-3806, DOI : 10.1090/S0002-9947-2015-05988-1 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00708973 .
Cf. the related Beamer presentation at HYP2012, Padua, Italy, 2012
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(2015) B. Andreianov, M. Bendahmane, A. Quarteroni and R. Ruiz Baier. Solvability Analysis and Numerical Approximation of Linearized Cardiac Electromechanics. M3AS Math. Methods Models Appl. Sci. 25 (5) (2015), pp. 959-993, DOI : 10.1142/S0218202515500244 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00865585
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(2015) B. Andreianov and D. Mitrović. Entropy conditions for scalar conservation laws with discontinuous flux revisited. Ann. Inst. H. Poincaré C Analyse Non Linéaire, 32 (6) (2015), pp.1307-1335, DOI : 10.1016/j.anihpc.2014.08.002 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00967848
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(2014) B. Andreianov, C. Donadello and M.D. Rosini. Crowd dynamics and conservation laws with non-local constraints. M3AS Math. Methods Models Appl. Sci. 24(13) (2014), pp. 2685-2722. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00816449
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(2014) B. Andreianov and C. Cancès. A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rocks media. Comput. Geosci., 18 (2) (2014) , pp.211-226. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00833522v1 Beamer presentation (SIAM Geosciences, Padua 2013)
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(2014) B. Andreianov, F. Lagoutière, N. Seguin and T. Takahashi. Well-posedness for a one-dimensional fluid-particle interaction model. SIAM J. Math. Anal., 46 (2) (2014), pp.1030-1052. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00789315
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(2014) B. Andreianov, K. Brenner and C. Cancès. Approximating the vanishing capillarity limit of two-phase flow in multi-dimensional heterogeneous porous medium. ZAMM Zeithschr. Angew. Math. Mech., 94(7-8), pp.655 – 667,DOI : 10.1002/zamm.201200218 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00744359 Beamer presentation at DFG-CNRS Workshop, Berlin, Germany, 2013
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(2013) B. Andreianov, M. Bendahmane and F. Hubert. On 3D DDFV discretization of gradient and divergence operators. Discrete functional analysis tools and applications. CMAM Comput. Meth. Appl. Math., 13 (4) (2013), pp.369-410, DOI : 10.1515/cmam-2013-0011 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00567342
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(2013) B. Andreianov and M. Gazibo Karimou. Entropy formulation of degenerate parabolic equation with zero-flux boundary condition. ZAMP Zeitschr. Angew. Math. Phys., 64 (5) (2013), pp 1471-1491, doi:10.1007/s00033-012-0297-6 . Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00697593.
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(2013) B. Andreianov and C. Cancès. Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks’ medium. Comput. Geosci., 17 (3) (2013), pp.551-572, doi:10.1007/s10596-012-9329-8. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00631584 Beamer presentation at MAMERN’11, Saidia, Morocco, 2011
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(2013) B. Andreianov, R. Eymard, M. Ghilani and N. Marhraoui. Finite volume approximation of degenerate two-phase flow model with unlimited air mobility. Num. Meth. PDEs, 29 (2) (2013), pp.441-474. Available as HAL preprint http://hal.archives-ouvertes.fr/hal-00606955 Beamer presentation (Nice 2012 ; Paris 6 2014)
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(2012) B. Andreianov, M. Bendahmane, F. Hubert and S. Krell. On 3D DDFV discretization of gradient and divergence operators. I. Meshing, operators and discrete duality. IMA J. Num. Anal., 32 (4) (2012), pp.1574-1603. Available as HAL preprint http://hal.archives-ouvertes.fr/hal-00355212
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(2012) B. Andreianov and C. Cancès. The Godunov scheme for scalar conservation laws with discontinuous bell-shaped flux functions. Applied Math. Letters, 25(11) (2012), pp.1844-1848. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00631586
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(2012) B. Andreianov and P. Wittbold. Convergence of approximate solutions to an elliptic-parabolic equation without the structure condition. NoDEA Nonlinear Diff. Equ. Appl., 19 (2012), no.6, pp.695-717. Available as HAL preprint http://hal.archives-ouvertes.fr/hal-00608521
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(2012) B. Andreianov and N. Seguin. Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes. Discr. Cont. Dyn. Syst. A 32(6) (2012), pp.1939-1964. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00576959 Beamer presentation (Bielefeld 2010, Edinburgh 2011)
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(2012) B. Andreianov and H. Labani. Preconditioning operators and L^1 attractor for a class of reaction-diffusion systems. Comm. Pure Appl. Analysis, 11(6) (2012) pp.2179-2199 ; available as HAL preprint http://hal.archives-ouvertes.fr/hal-00522783 Beamer presentation (Bordeaux 2010)
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(2012) B. Andreianov and N. Igbida. On uniqueness techniques for degenerate convection-diffusion problems. Int. J. Dyn. Syst. Diff. Equ. 4 (1/2) (2012), pp.3-34 ; available at http://hal.archives-ouvertes.fr/hal-00553819.
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(2011) B. Andreianov, M. Bendahmane and M. Saad. Finite volume methods for degenerate chemotaxis model. J. Comput. Appl. Math. 235 (2011), pp.4015-4031.
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(2011) B. Andreianov, M. Bendahmane, K.H. Karlsen and Ch. Pierre. Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Networks Heter. Media, 6 (2011), no.2, pp.195-240. Beamer presentation (Nantes 2009)
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(2011) B. Andreianov, K.H. Karlsen and N.H. Risebro. A theory of L^1-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201 (2011), no.1, pp.27-86. Beamer presentation (HYP2010 Beijing, China ; Jaca 2010)
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(2011) B. Andreianov, M. Bendahmane and R. Ruiz Baier. Analysis of a finite volume method for a cross-diffusion model in population dynamics. M3AS Math. Models Methods Appl. Sci. 21 (2011), no.2, pp.307-344. Beamer presentation (Rennes 2010)
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(2010) B. Andreianov, K.H. Karlsen and N.H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Netw. Heterog. Media 5 (2010), no. 3, pp.617-633.
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(2010) B. Andreianov, F. Lagoutière, N. Seguin and T. Takahashi. Small solids in an inviscid fluid. Netw. Heterog. Media 5 (2010), no. 3, pp.385-404. Beamer presentation (Bielefeld 2010)
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(2010) N. Alibaud and B. Andreianov. Non-uniqueness of weak solutions for the fractal Burgers equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 4, pp.997-1016. Beamer presentation (Berlin 2009, Parma 2010)
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(2010) B. Andreianov, P. Goatin and N. Seguin. Finite volume schemes for locally constrained conservation laws. Numerische Math. 115 (2010), no. 4, pp.609-645. Beamer presentation (Clermont-Ferrand 2009, Orsay 2009)
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(2010) B. Andreianov, M. Bendahmane and S. Ouaro. Structural stability for variable exponent elliptic problems. II. The p(u)-Laplacian and coupled problems. Nonlinear Anal. Ser. A, 72 (2010), no. 12, pp.4649-4660. Beamer presentation (Oslo 2008, Toulouse 2009)
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(2010) B. Andreianov, M. Bendahmane and S. Ouaro. Structural stability for variable exponent elliptic problems. I : the p(x)-Laplacian kind problems. Nonlinear Anal. Ser. A, 73 (2010), no. 1, pp.2-24. Beamer presentation (Oslo 2008, Toulouse 2009)
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(2010) B. Andreianov, M. Bendahmane and K.H. Karlsen. Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations. J. Hyperbolic Diff. Equ. 7 (2010), no. 1, pp.1-67. Beamer presentation (CIRM, Luminy 2011)
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(2010) B. Andreianov and M. Maliki. A note on uniqueness of entropy solutions to degenerate parabolic equations in R^N. NoDEA Nonlinear Diff. Equ. Appl. 17 (2010), no. 1, pp.109-118.
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(2009) B. Andreianov, M. Bendahmane, K.H. Karlsen and S. Ouaro. Well-posedness results for triply nonlinear degenerate parabolic equations. J. Differ. Equ. 247 (2009), no. 1, pp.277-302.
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(2008) B. Andreianov, K. Sbihi and P. Wittbold. Well-posedness for some elliptic-parabolic problems with nonlinear boundary conditions. J. Evol. Equ. 8 (2008), no. 3, pp.449-490. Beamer presentation (Valencia, Mazón’60 congress)
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(2007) B. Andreianov and N. Igbida. Uniqueness for the Dirichlet elliptic-parabolic problem. Proc. Royal Soc. Edinburgh, 137A (2007), pp.1119-1133.
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(2007) B. Andreianov, F. Boyer and F. Hubert. Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D meshes. Num. Methods PDE 23 (2007), no.1, pp.145-195. Beamer presentation at FVCA 4, Marrakesh, Morocco, 2005
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(2006) B. Andreianov and N. Igbida. Revising Uniqueness for a Nonlinear Diffusion-Convection Equation. J. Differ. Equ. 227 (2006), no.1, pp.69-79. Also consult the Erratum to the paper where some missing arguments are provided.
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(2006) B. Andreianov, F. Boyer and F. Hubert. On finite volume approximation of regular solutions of the p-laplacian. IMA J. Numer. Anal. 26 (2006), no.3, pp.472-502.
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(2005) B. Andreianov, F. Boyer and F. Hubert. Besov regularity and new error estimates for finite volume approximations of the p-laplacian. Numerische Math. 100 (2005), no.4, pp.565-592.
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(2004) B. Andreianov, F. Boyer and F. Hubert. Finite volume schemes for the p-Laplacian on Cartesian meshes. M2AN Math. Model. Numer. Anal. 38 (2004), no.6, pp.931-959.
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(2004) B. Andreianov and F. Bouhsiss. Uniqueness for an elliptic-parabolic problem with Neumann boundary condition. J. Evol. Equ. 4 (2004), no.2, pp.273-295.
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(2004) B. Andreianov, M. Gutnic and P. Wittbold. Convergence of finite volume approximations for a nonlinear elliptic-parabolic problem : a “continuous” approach. SIAM J. Numer. Anal. 42 (2004), no.1, pp.228-251.
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(2003) B. Andreyanov. On limits of solutions of the Riemann problem for a system of isentropic gas dynamics with viscosity in Euler coordinates. (Russian) Mat. Sb. 194 (2003), no.6, pp.3-22 ; Engl. translation in Sb. Math. 194 (2003), no. 5-6, pp.793-811.
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(2000) B. Andreianov, Ph. Bénilan and S.N. Kruzhkov. L^1-theory of scalar conservation law with continuous flux function. J. Funct. Anal. 171 (2000), no.1, pp.15-33.
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(1999) B. Andreianov. The Riemann problem for a p-system with continuous flux function. Ann. Fac. Sci. Toulouse 8 (1999), no.3, pp.353-367.
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(1999) B. Andreyanov. Vanishing viscosity method and explicit formulae for solutions of the Riemann problem for scalar quasilinear conservation law. (Russian). Vestn. Mosc. Univ. I : Math.&Mech. 71 (1999), no.1, pp.3-8. Transl. in Moscow Univ. Math. Bull. 54 (1999), no. 1, 1–6 ; available as Chapter I.1 of my Ph.D. Thesis
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(1997) B. Andreyanov. Solutions auto-similaires du problème de Riemann pour une loi de conservation scalaire quasilinéaire à fonction de flux continue avec la viscosité t u_xx. Publ. Math. Besançon – Anal. non linéaire, no.15, (1997), pp.127-131.
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CRAS Paris notes, proceedings and chapters of monographs (peer-reviewed)

(2019) B. Andreianov and M.D. Rosini. Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic, to appear. In M. Lachowicz et al. eds., , Springer Proc. in Math. and Stat. Vol.??, 2019, paper no.12 Available as preprint HAL http://hal.archives-ouvertes.fr/hal-02197482
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(2018) B. Andreianov, C. Donadello, U. Razafison, M. Rosini. One-dimensional conservation laws with non-local point constraints on the flux. In : Crowd Dynamics, Volume 1 – Theory, Models, and Safety Problems (N. Bellomo, L. Gibelli eds.), Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, 2018, pp.103-135. DOI : 10.1007/978-3-030-05129-7_5
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(2017) B. Andreianov, M. Kramar Fijavž, A. Peperko, E. Sikolya. Erratum to : Semigroups of max-plus linear operators. Semigroup Forum 94 (2017), no.2, pp 477—479, DOI : 10.1007/s00233-017-9870-9 .
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(2015) B. Andreianov. New approaches to describing admissibility of solutions of scalar conservation laws with discontinuous flux. ESAIM : Proc. and Surveys 50 (2015), pp.40-65, DOI : http://dx.doi.org/10.1051/proc/201550003 Available as preprint HAL http://hal.archives-ouvertes.fr/hal-01109040
Beamer presentation at ICJ Lyon 2019
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(2015) B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini. Riemann problems with non—local point constraints and capacity drop, Math. Biosci. Engineering 12(2) (2015), pp.259-268. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00959974
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(2014) B. Andreianov and M. Karimou Gazibo. Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition, In Führmann et al., eds, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects Springer Proc. Math. Stat. Vol. 77, 2014, pp.303-311. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00950142
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(2014) B. Andreianov. One-dimensional conservation law with boundary conditions : general results and spatially inhomogeneous case, In F. Ancona et al., eds. Hyperbolic Problems : Theory, Numerics, Applications, Proceedings of 14th HYP conference in Padua, AIMS series in Appl. Math. Vol.8, pp.259-267. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00761664
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(2014) B. Andreianov. Semigroup approach to conservation laws with discontinuous flux. In G-Q. Chen, H. Holden and K.H. Karlsen, eds., Springer Proc. in Math. and Stat. Vol.49, 2014, pp.1—22. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00698581
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(2012) B. Andreianov, R. Eymard, M. Ghilani and N. Marhraoui. On intrinsic formulation and well-posedness of a singular limit of two-phase flow equations in porous media. Monografias de la Real Academia de Ciencias de Zaragoza 38 (2012), pp.21-34. Available as preprint HAL http://hal.archives-ouvertes.fr/hal-00606948 Beamer presentation (Nice 2012 ; Paris 6 2014)
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(2012) B. Andreianov. Dissipative coupling of scalar conservation laws across an interface : theory and applications. In : Proceedings of the HYP2010 conference in Beijing, Ta-Tsien Li and Song Jiang, eds. Contemp. Appl. Math., Vol. 17, World Scientific, Singapore, 2012, pp.123-135. Beamer presentation (HYP2010 Beijing, China ; Jaca 2010)
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(2011) B. Andreianov, F. Hubert, and S. Krell. Benchmark 3D : a version of the DDFV scheme with cell/vertex unknowns on general meshes. In : Proceedings of Finite Volume for Complex Applications VI, Prague, Springer, 2011, Volume 4, Part 3, pp.937-948 ( DOI : 10.1007/978-3-642-20671-9_91 ) ; available as HAL preprint http://hal.archives-ouvertes.fr/hal-00572732
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(2011) B. Andreianov. Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs. In : Proceedings of Finite Volume for Complex Applications VI, Prague, Springer, 2011, Volume 4, Part 1, pp.21-29 ( DOI : 10.1007/978-3-642-20671-9_3 ) ; available as HAL preprint http://hal.archives-ouvertes.fr/hal-00561344 Beamer presentation at FVCA 6, Prague, Czech Republic, 2011
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(2010) N. Alibaud, B. Andreianov and M. Bendahmane. Renormalized solutions of the fractional Laplace equation. C. R. Math. Acad. Sci. Paris Sér. I, 348 (2010), no. 13-14, pp.759-762. Beamer presentation (Bielefeld 2011)
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(2008) B. Andreianov, M. Bendahmane, and K.H. Karlsen. A gradient reconstruction formula for finite volume schemes and discrete duality. In : Proceedings of Finite Volumes for Complex Applications V, pp.161-168, ISTE, London, 2008.
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(2008) B. Andreianov and K. Sbihi. Strong boundary traces and well-posedness for scalar conservation laws with dissipative boundary conditions. In : Hyperbolic problems : theory, numerics, applications, HYP2008 Lyon Proceedings, pp.937-945, Springer, Berlin, 2008.
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(2007) B. Andreianov and K. Sbihi. Scalar conservation laws with nonlinear boundary conditions. C. R. Acad. Sci. Paris, Ser. I, 345 (2007), pp.431-434.
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(2007) B. Andreianov, F. Boyer and F. Hubert. Discrete Besov framework for finite volume approximation of the p-laplacian on non-uniform cartesian grids. ESAIM Proceedings 18 (2007), pp.1-10.
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(2005) B. Andreianov, F. Boyer and F. Hubert. “Duplex” finite-volume schemes for nonlinear elliptic problems on general 2D meshes. In : Proceedings of Finite Volumes for Complex Applications IV, Marrakech, pp. 365-376, Ed. F. Benkhaldoun, D. Ouazar et S. Raghay, Hermes Science (2005). Available as Beamer presentation at FVCA 4, Marrakesh, Morocco, 2005
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(2001) B. Andreianov, M. Gutnic and P. Wittbold. L’approche “continue” pour une méthode de volumes finis. C. R. Acad. Sci. Paris Sér. I, 332 (2001), no.5, pp.477-482.
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Other notes and proceedings

(2013) B. Andreianov. Techniques entropiques et renormalisation pour les opérateurs de diffusion fractionnaire. Actes du 3ème colloque EDP-Normandie, Le Havre, Oct. 2012.

Preprints, unpublished works

(Preprint) B. Andreianov and M. Karimou Gazibo. Solutions processus intégrales des équations d’évolution abstraites et application à l’approximation numérique d’un problème parabolique dégénéré. [ Integral-process solutions of abstract evolution equations and application to numerical approximation of a degenerate parabolic boundary-value problem. ]. Preprint HAL http://hal.archives-ouvertes.fr/hal-00857478
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(Preprint) B. Andreianov. Elliptic-parabolic problems : existence and structural stability of weak solutions. Unpublished ; available as Chapter II.1 of my Ph.D. Thesis.

Translation (from Russian)

(Translation) G.A. Chechkin et A.Yu. Goritsky, S.N. Kruzhkov lectures on first-order quasilinear PDEs. In E. Emmrich, P. Wittbold, eds., Analytical and Numerical Aspects of PDEs, DeGruyter, Berlin, 2009. Available at http://hal.archives-ouvertes.fr/hal-00363287

Manuscripts

Ph.D. Thesis / Thèse de Doctorat
Habilitation Thesis / Mémoire HDR :
Manuscript and Slides
Lectures “Finite Volumes for p-Laplacian”, Berlin and Jaca, 2010