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arXiv · 0805.2314

Long-time extinction of solutions of some semilinear parabolic equations

Yves Belaud·Andrey Shishkov
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Abstract

We study the long time behaviour of solutions of semi-linear parabolic equation of the following type $\partial_t u-Δu+a_0(x)u^q=0$ where $a_0(x) \geq d_0 \exp(\frac{ω(|x|)}{|x|^2})$, $d_0>0$, $1>q>0$ and $ω$ a positive continuous radial function. We give a Dini-like condition on the function $ω$ by two different method which implies that any solution of the above equation vanishes in a finite time. The first one is a variant of a local energy method and the second one is derived from semi-classical limits of some Schrödinger operators.

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Yves Belaud, Andrey Shishkov. 2008-05-15. Long-time extinction of solutions of some semilinear parabolic equations. https://arxiv.org/abs/0805.2314

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