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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 $\gf(0)=\infty$.
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Submitted on : Wednesday, September 9, 2015 - 3:25:10 PM
Last modification on : Tuesday, August 13, 2019 - 2:00:02 PM
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  • HAL Id : hal-01136836, version 3
  • ARXIV : 1503.08532

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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⟩

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