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.