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Admissible Initial Growth for Diffusion Equations with Weakly Superlinear Absorption by Shishkov, Andrey; Véron, Laurent is a scholarly article available to read on EtoBox.

What is Admissible Initial Growth for Diffusion Equations with Weakly Superlinear Absorption about?

We study the admissible growth at infinity of initial data of positive solutions of $\prt\_t u-\Gd u+f(u)=0$ in $\BBR\_+\ti\BBR^N$ when $f(u)$ is a continuous function, {\it mildly} superlinear at infinity, the model case being $f(u)=u\ln^\ga (1+u)$ with $1\textless{}\ga\textless{}2$. We prove in particular that if the growth of the initial data at infinity is too strong, there is no more diffusion and the corresponding solution satisfies the ODE problem $\prt\_t \gf+f(\gf)=0$ on $\BBR\_+$ with $\gf(0)=\infty$.

Author

Shishkov, Andrey; Véron, Laurent

Published

2015

Language

EN