Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces

Azeddine Aissaoui Fqayeh ; Abdelmoujib Benkirane ; Mostafa El Moumni

Applicationes Mathematicae, Tome 41 (2014), p. 185-193 / Harvested from The Polish Digital Mathematics Library

Résumé

We discuss the existence of entropy solution for the strongly nonlinear unilateral parabolic inequalities associated to the nonlinear parabolic equations ∂u/∂t - div(a(x,t,u,∇u) + Φ(u)) + g(u)M(|∇u|) = μ in Q, in the framework of Orlicz-Sobolev spaces without any restriction on the N-function of the Orlicz spaces, where -div(a(x,t,u,∇u)) is a Leray-Lions operator and $Φ ∈ C⁰(ℝ,ℝ^{N})$. The function g(u)M(|∇u|) is a nonlinear lower order term with natural growth with respect to |∇u|, without satisfying the sign condition, and the datum μ belongs to L¹(Q) or $L¹(Q) + W^{-1,x} E_{M̅}(Q)$.

Détail

Publié le : 2014-01-01

Zbl 1307.35147

EUDML-ID : urn:eudml:doc:279886