2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 53-83.

Sets of admissible initial data for porous-medium equations with absorptions

Emmanuel Chasseigne & Juan Luis Vazquez

Abstract:
In this article, we study a porous-medium equation with absorption in $\mathbb{R}^{N}\times (0,T)$ or in $\Omega \times (0,T)$:
$$ u_{t}-\Delta u^{m}+u^{p}=0\,. $$
We give a rather complete qualitative picture of the initial trace problem in all the range $m$ greater than 1, $p\geq 0$. We consider nonnegative Borel measures as initial data (not necessarily locally bounded) and discuss whether or not the Cauchy problem admits a solution. In the case of non-admissible data we prove the existence of some projection operators which map any Borel measure to an admissible measure for this equation.

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Emmanuel Chasseigne
Laboratoire de Mathematiques et Physique Theorique
Universite de Tours
Parc de Grandmont, 37200 Tours, France.
E-mail: echasseigne@univ-tours.fr
Juan Luis Vazquez
Departamento de Matematicas
Universidad Autonoma de Madrid
28046 Madrid, Spain.
E-mail: juanluis.vazquez@uam.es

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