Agenda de l’IDP

Séminaire d'Analyse

Local and global properties of solutions of heat equation with weakly superlinear absorption
Laurent Véron (travail en collaboration avec Nguyen Phuoc TAI)
jeudi 07 octobre 2010 11:15 -  Tours -  Salle 2290 (Bât E2)

Résumé :
We study the limit, when $k\to\infty$ of the solutions of $ \prt_tu-\Delta u+f(u)=0$ in $\BBR^N\ti(0,\infty)$ with initial data $k\gd$, when $f$ is a positive superlinear increasing function. We prove that there exist essentially three types of possible behaviour according $f^{-1}$ and $F^{-1/2}$ belong or not to $L^1(1,\infty)$, where $F(t)=\int_0^t f(s)ds$. We use these results for providing a new and more general construction of the initial trace and some uniqueness and non-uniqueness results for solutions with unbounded initial data. P.S. L'exposé sera en français, mais les transparents en anglais

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