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

• Autorzy: Azeddine Aissaoui Fqayeh , Abdelmoujib Benkirane , Mostafa El Moumni
• Języki publikacji: EN

Abstrakty

EN

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 $L¹(Q) + W^{-1,x} E_{M̅}(Q)$.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 2-3
• Strony: 185-193

Daty

wydano

2014

Twórcy

autor

Azeddine Aissaoui Fqayeh

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796 Atlas, Fez, Morocco

autor

Abdelmoujib Benkirane

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796 Atlas, Fez, Morocco

autor

Mostafa El Moumni

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796 Atlas, Fez, Morocco

Identyfikatory

DOI

10.4064/am41-2-6