Electronic Journal of Differential Equations,
Conference 08 (2002), pp. 53-83

Title: Sets of admissible initial data for porous-medium equations with absorption

Authors: Emmanuel Chasseigne (Univ. Autonoma de Madrid, Madrid, Spain)
 Juan Luis Vazquez (Univ. Autonoma de Madrid, Madrid, Spain)

 
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 $m>1$, $p\geqslant 0$.
 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.

Published October 21, 2002.
Math Subject Classifications: 35K55, 35K65.
Key Words: Initial trace; Borel  measures; initial projection; singular solution.