# M. Chrif(CRMEF), Meknes, Maroc : Centre Régional des Métiers de l'Education et de la Formation · Mathématiques

M. Chrif

Professeur de l'enseignement supérieur

## About

23

Publications

2,960

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107

Citations

Citations since 2017

Introduction

**Skills and Expertise**

## Publications

Publications (23)

This paper is concerned with the study of the nonlinear Dirichlet parabolic problem in a bounded subset \(\Omega \subset I\!\!R^N\)$$\begin{aligned} u_{t} + Au + g(x,t, u, \nabla u) = f - \text{ div } \phi (u), \end{aligned}$$where A is an operator of Leray-Lions type acted from the parabolic anisotropic space \(L^{\vec {p}}(0,T;W_{0}^{1,\vec {p}}(...

In this paper we are concerned with the study of a class of second-order quasilinear parabolic equations involving Leray-Lions type operators with anisotropic growth conditions. By an approximation argument, we estabilsh the existence of entropy solutions in the framework of anisotropic parabolic Sobolev spaces when the initial condition and the da...

In this paper, we prove the existence of solutions for the strongly nonlinear equation of the type $$Au+g(x,u)=f$$ where $A$ is an elliptic operator of infinite order from a functional Sobolev spaces of infinite order with variables exponents to its dual. $g(x, s)$ is a lower order term satisfying essentially a sign condition on s and the second te...

The existence , regularity of pds and its applications
numerical simulations
and motivations

This paper is devoted to the study of the existence of solutions for the strongly nonlinear parabolic equation ∂u/∂t +Au+g(x, t,u) = f (x, t), where A is a Leray-Lions operator acted from V∞,p(.)(aα,QT ) into its dual. The nonlinear term g satisfies growth and sign conditions and the datum f is assumed to be in the dual space V-∞,p'(.)(aα,QT ).

In this paper, we give an approximation result in some anisotropic Sobolev
space. We also describe the action of some distributions in the dual and we men-
tion two applications to some strongly nonlinear anisotropic elliptic boundary value
problems.

We prove the existence of weak solutions for the strongly nonlinear parabolic problem
in the anisotropic Sobolev space , where the data f are assumed to be in the dual, and the nonlinear term g(x, t, s) has growth and sign conditions on s .

In this paper, we obtain the existence of weak solutions to a class of strongly anisotropic nonlinear elliptic boundary-value problems with nonlinear lower-order term with natural growth in an appropriate anisotropic function space. We investigate the cases where the right hand side term is regular or to be in L1: A uniqueness result is also given...

In this work, we are interested in the existence of solutions for strongly anisotropic non-linear problems with non-standard growth conditions in the framework of Sobolev spaces of infinite order with variables exponents.

In this paper an existence result is presented for solution of a parabolic boundary value problem under Dirichlet null boundary conditions for a class of general equations of infinite order with strongly nonlinear perturbation terms.

We prove an existence result of a nonlinear parabolic equation under Dirichlet null boundary conditions in Sobolev spaces of infinite order, where the second member belongs to .

We prove the existence of weak solutions to some nonlinear elliptic equations governed by an anisotropic operator mapping an appropriate function space to its dual. A sign condition with no growth restrictions with respect to the variable solution is imposed to a perturbed nonlinear term to the operator. The data is considered to be close to L 1 .

We prove the existence of weak solutions to some nonlinear elliptic equations governed by an anisotropic operator mapping an appropriate function space to its dual. A sign condition with no growth restrictions with respect to the variable solution is imposed to a perturbed nonlinear term to the operator. The data is considered to be close to L^1 .

In this paper, we give an approximation result in some anisotropic Sobolev space. We also describe the action of some distributions in the dual and we mention two applications to some strongly nonlinear anisotropic elliptic boundary value problems.

Uing an equivalent variational approach to a recent B. Ricceri’s three critical points theorem [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, A, 3084–3089 (2009; Zbl 1214.47079)], we obtain the existence of at least three non-trivial solutions of a Neumann problem for elliptic equations with variable exponents.

Generalized Sobolev spaces are considered. The existence of solutions for strongly nonlinear equations of infinite order of the form Au+g(x,u)=f is established. Here, A is an operator from a Sobolev type space to its dual and g(x,s) is a lower order term satisfying a sign condition on s. We consider the case where the data f belongs to L 1 .

We consider the strongly nonlinear boundary value problem,
Au+g(x,u)=fAu+g(x,u)=f
where A is an elliptic operator of finite or infinite order. We introduce anisotropic weighted Sobolev spaces and we show under a
certain sign condition of the Carathéodory function g without assuming any growth restrictions, the existence of the weak solutions.

In this paper, we prove the existence of solutions for the strongly nonlinear equation of the type Au + g(x, u) = f where A is an elliptic operator of infinite order from a functional space of Sobolev type to its dual. g(x, s) is a lower order term satisfying essentially a sign condition on s and the second term f belongs to L-1( Omega).

We deal with the existence and uniqueness of weak solutions for a class of strongly nonlinear boundary value problems of higher order with L1 data in anisotropic-weighted Sobolev spaces of infinite order. Copyright © 2009 John Wiley & Sons, Ltd.

In this article, we shall be concerned with the existence of solutions for the strongly non-linear boundary value problem: where A is an elliptic operator of finite order defined from an anisotropic Sobolev space of order m to its dual, g is a Carathéodory function satisfying essentially a sign condition on u with no growth restrictions and f belon...

In this article, we shall be concerned with the existence of solutions for the
strongly non-linear boundary value problem:
Au þ gðx, uÞ ¼ f,
where A is an elliptic operator of finite order defined from an anisotropic Sobolev
space of order m to its dual, g is a Carathe´odory function satisfying essentially
a sign condition on u with no growth restr...

In this work, generalized Sobolev spaces and Sobolev spaces of infinite order are considered. Existence of solutions for strongly nonlinear equation of infinite order of the form Au + g(x, u) = f is established. Here A is an elliptic operator from a functional space of Sobolev type to its dual and g(x, s) is a lower order term satisfying a sign con...