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)
Thursday 07 October 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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