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

Azeddine Aissaoui Fqayeh, Abdelmoujib Benkirane, and Mostafa El Moumni. "Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces." Applicationes Mathematicae 41.2-3 (2014): 185-193. <http://eudml.org/doc/279886>.

@article{AzeddineAissaouiFqayeh2014,
abstract = {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 $L¹(Q) + W^\{-1,x\} E_\{M̅\}(Q)$.},
author = {Azeddine Aissaoui Fqayeh, Abdelmoujib Benkirane, Mostafa El Moumni},
journal = {Applicationes Mathematicae},
keywords = {-data; Leray-Lions operator; nonlinear lower order term},
language = {eng},
number = {2-3},
pages = {185-193},
title = {Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces},
url = {http://eudml.org/doc/279886},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Azeddine Aissaoui Fqayeh
AU - Abdelmoujib Benkirane
AU - Mostafa El Moumni
TI - Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 2-3
SP - 185
EP - 193
AB - 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 $L¹(Q) + W^{-1,x} E_{M̅}(Q)$.
LA - eng
KW - -data; Leray-Lions operator; nonlinear lower order term
UR - http://eudml.org/doc/279886
ER -