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

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Aissaoui Fqayeh A., Benkirane A., El Moumni M.

Applicationes Mathematicae

2014

tom 41

nr 2-3

185-193

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 $L¹(Q) + W^{-1,x} E_{M̅}(Q)$.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Aissaoui Fqayeh A.

1 Benkirane A.

1 El Moumni M.

1 2014

Wyniki wyszukiwania

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