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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2018

Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

Résumé

We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: (PT) ut -∇·a(x,∇u) = f(x,u)in QT =def(0,T) × ω,u = 0 on =T =def(0,T) × ∂ω,u(0,x) = u0(x) in ω, which involves a quasilinear elliptic operator of Leray-Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as t →∞. © 2018 World Scientific Publishing Company.
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Dates et versions

hal-01759880 , version 1 (05-04-2018)

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Jacques Giacomoni, Guillaume Warnault, V. Radulescu. Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization. Communications in Contemporary Mathematics, 2018, 20 (8), pp.1750065. ⟨10.1142/S0219199717500651⟩. ⟨hal-01759880⟩
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