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Pré-Publication, Document De Travail Année : 2016

Extinction in a finite time for solutions of large classes of Parabolic Equations involving p-Laplacian

Résumé

We study the property of extinction in a finite time for nonnegative solutions of 1/q ∂t (u q) − delta_p 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 ⊂ R^N a bounded domain of R^N (N ≥ 1). Necessary and sufficient conditions are provided with the help of a family of infimum. When p > 1 + q, the threshold is for power functions but for p = 1 + q, it happens extinction in a finite time for very flat functions.
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Dates et versions

hal-01413930 , version 1 (11-12-2016)

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  • HAL Id : hal-01413930 , version 1

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Y Belaud, A Shishkov. Extinction in a finite time for solutions of large classes of Parabolic Equations involving p-Laplacian. 2016. ⟨hal-01413930⟩
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