PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Volume 41 / 2014

Azeddine Aissaoui Fqayeh, Abdelmoujib Benkirane, Mostafa El Moumni Applicationes Mathematicae 41 (2014), 185-193 MSC: Primary 46E30; Secondary 35K85. DOI: 10.4064/am41-2-6

Abstract

We discuss the existence of entropy solution for the strongly nonlinear unilateral parabolic inequalities associated to the nonlinear parabolic equations $\frac {\partial u}{\partial t}-{\rm div}(a(x,t,u,\nabla u)+\varPhi (u)) + g(u)M(|\nabla u|) = \mu $ in $Q,$ in the framework of Orlicz–Sobolev spaces without any restriction on the $N$-function of the Orlicz spaces, where $-{\rm div} (a(x,t,u,\nabla u))$ is a Leray–Lions operator and $\varPhi \in C^{0}(\mathbb {R},\mathbb {R}^{N})$. The function $g(u)M(|\nabla u|)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, without satisfying the sign condition, and the datum $\mu $ belongs to $L^1(Q)$ or $L^1(Q)+W^{-1,x}E_{\overline {M}}(Q)$.

Authors

  • Azeddine Aissaoui FqayehLaboratory LAMA
    Department of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University Sidi Mohamed Ben Abdellah
    P.O. Box 1796 Atlas
    Fez, Morocco
    e-mail
  • Abdelmoujib BenkiraneLaboratory LAMA
    Department of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University Sidi Mohamed Ben Abdellah
    P.O. Box 1796 Atlas
    Fez, Morocco
    e-mail
  • Mostafa El MoumniLaboratory LAMA
    Department of Mathematics
    Faculty of Sciences Dhar El Mahraz
    University Sidi Mohamed Ben Abdellah
    P.O. Box 1796 Atlas
    Fez, Morocco
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image