# Admissible initial growth for diffusion equations with weakly superlinear absorption

Abstract : 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 $1<\ga<2$. 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 $\gf(0)=\infty$.
Keywords :
Document type :
Journal articles

Cited literature [8 references]

https://hal.archives-ouvertes.fr/hal-01136836
Contributor : Laurent Veron <>
Submitted on : Wednesday, September 9, 2015 - 3:25:10 PM
Last modification on : Tuesday, August 13, 2019 - 2:00:02 PM
Document(s) archivé(s) le : Monday, December 28, 2015 - 11:19:03 PM

### Files

Files produced by the author(s)

### Identifiers

• HAL Id : hal-01136836, version 3
• ARXIV : 1503.08532

### Citation

Andrey Shishkov, Laurent Véron. Admissible initial growth for diffusion equations with weakly superlinear absorption. Communications in Contemporary Mathematics, World Scientific Publishing, 2015, 18 (5), pp.13. ⟨hal-01136836v3⟩

Record views