Initial trace for a porous medium equation: II. The critical absorption term

Article type: Research Article

Authors: Chasseigne, Emmanuel

Affiliations: Faculté des Sciences et Techniques, Parc de Grandmont, F‐37200 Tours, France E‐mail: echasseigne@univ‐tours.fr

Abstract: We consider the following non linear diffusion equation with critical absorption exponent: u_{t}-\Delta u^{m}+u^{m}=0, m>1, in a bounded set \varOmega and in \mathbb{R}^{N}. In the whole space, we give optimal conditions on measure initial data to have existence and uniqueness, and we study singular solutions, which explode in \varOmega when t\rightarrow0. The problem of the initial trace is also completely addressed, and we derive estimates for the initial trace of continuous solutions.

Journal: Asymptotic Analysis, vol. 24, no. 1, pp. 37-72, 2000