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Journal Articles Asymptotic Analysis Year : 2021

Extinction in a finite time for solutions of a class of quasilinear parabolic equations

Abstract

We study the property of extinction in a finite time for nonnegative solutions of 1 q ∂ ∂ t ( u q ) − ∇ ( | ∇ u | p − 2 ∇ u ) + a ( x ) u λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p ⩾ 1 + q, p ⩾ 2, a ( x ) ⩾ 0 and Ω a bounded domain of R N ( N ⩾ 1). We prove some necessary and sufficient conditions. The threshold is for power functions when p > 1 + q while finite time extinction occurs for very flat potentials a ( x ) when p = 1 + q.
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Dates and versions

hal-03922036 , version 1 (04-01-2023)

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Y. Belaud, A. Shishkov. Extinction in a finite time for solutions of a class of quasilinear parabolic equations. Asymptotic Analysis, 2021, 127 (1-2), pp.97-119. ⟨10.3233/ASY-211674⟩. ⟨hal-03922036⟩
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