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

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.

Show me the PDF file (340K), TEX file, and other files for this article.

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

Return to the table of contents for this conference.
Return to the EJDE web page