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5: Paper Source PDF document

Paper's Title:

Strongly Nonlinear Variational Parabolic Problems in Weighted Sobolev Spaces


L. Aharouch, E. Azroul and M. Rhoudaf

Dép. Math. Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fés,


In this paper , we study the existence of a weak solutions for the initial-boundary value problems of the strongly nonlinear degenerated parabolic equation,

∂u +A(u)+g(x,t,u,∇ u)=f

where A is a Leray-lions operator acted from Lp(0,T,W01,p(Ώ,w)) into its dual. g(x,t,u,∇ u) is a nonlinear term with critical growth condition with respect to ∇ u and no growth with respect to u. The source term f is assumed to belong to Lp'(0,T,W-1,p'(Ώ,w*)).

2: Paper Source PDF document

Paper's Title:

On some Strongly Nonlinear Elliptic Problems in -data with a Nonlinearity Having a Constant Sign in Orlicz Spaces via Penalization Methods


E. Azroul, A. Benkirane and M. Rhoudaf

Dep. Math., Faculté des Sciences Dhar-Mahraz,
B.P 1796 Atlas Fès,

Departement of Mathematics,
Faculty of Sciences and Techniques of Tangier,
B.P. 416, Tangier,


This paper is concerned with the existence result of the unilateral problem associated to the equations of the type

in Orlicz spaces, without assuming the sign condition in the nonlinearity g. The source term f belongs to L¹(Ώ).

1: Paper Source PDF document

Paper's Title:

Renormalized Solutions for Nonlinear Parabolic Equation with Lower Order Terms


A. Aberqi1, J. Bennouna1, M. Mekkour1 and H. Redwane2

1Université Sidi Mohammed Ben Abdellah,
Département de Mathématiques,
Laboratoire LAMA, Faculté des Sciences Dhar-Mahrez,
B.P 1796 Atlas Fés,

2Faculté des Sciences Juridiques, Economiques et Sociales,
Université Hassan 1, B.P. 784. Settat,


In this paper, we study the existence of renormalized solutions for the nonlinear parabolic problem: ,where the right side belongs to L1(Ω×(0,T)) and b(u) is unbounded function of u, the term div(a(x,t,u,u)) is a Leray--Lions operator and the function φ is a nonlinear lower order and satisfy only the growth condition.

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