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

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 an...

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Bibliographic Details
Published inAsymptotic analysis Vol. 127; no. 1-2; pp. 97 - 119
Main Authors Belaud, Y., Shishkov, A.
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2022
IOS Press
Subjects
Analysis of PDEs
Boundary conditions
Dirichlet problem
Extinction
Mathematics
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Summary: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.
ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-211674