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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2014

Complete quenching for a quasilinear parabolic equation

Résumé

We study the homogeneous Dirichlet problem for the quasilinear parabolic equation with the singular absorption term∂tu-δpu+1u>0u-β=f(x,u)in QT=(0,T)×Ω. Here Ω⊂Rd, d≥1, is a bounded domain, δpu=div(|∇;u|p-2∇;u) is the p-Laplace operator and β∈(0, 1) is a given parameter. It is assumed that the initial datum satisfies the conditionsu0∈W01,p(Ω)∩L∞(Ω),u0≥0 a.e. in Ω. The right-hand side f:Ω×R→[0,∞) is a Carathéodory function satisfying the power growth conditions: 0≤f(x, s)≤α|s|q-1+Cα with positive constants α, Cα and q≥1. We establish conditions of local and global in time existence of nonnegative solutions and show that if q≤p and α and Cα are sufficiently small, then every global solution vanishes in a finite time a.e. in Ω. *Quasilinear parabolic equations with singular absorption terms.*Existence of weak bounded solutions.*Sufficient conditions of the complete quenching in a finite time.*Blow-up in a finite time. © 2013 Elsevier Inc.

Dates et versions

hal-00985040 , version 1 (29-04-2014)

Identifiants

Citer

Jacques Giacomoni, P. Sauvy, S. Shmarev. Complete quenching for a quasilinear parabolic equation. Journal of Mathematical Analysis and Applications, 2014, 410 (2), pp.607-624. ⟨10.1016/j.jmaa.2013.08.051⟩. ⟨hal-00985040⟩
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