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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
On some Strongly Nonlinear Elliptic Problems
in L¹-data with a Nonlinearity Having a Constant Sign in Orlicz
Spaces via Penalization Methods
Author(s):
E. Azroul, A. Benkirane and M. Rhoudaf
Dep. Math., Faculté des Sciences
Dhar-Mahraz,
B.P 1796 Atlas Fès,
Maroc
Departement of Mathematics,
Faculty of Sciences and Techniques of Tangier,
B.P. 416, Tangier,
Morocco.
rhoudaf_mohamed@yahoo.fr
Abstract:
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).
Paper's Title:
Strongly Nonlinear Variational Parabolic Problems in Weighted Sobolev Spaces
Author(s):
L. Aharouch, E. Azroul and M. Rhoudaf
Dép. Math. Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fés,
Maroc.
rhoudaf_mohamed@yahoo.fr
Abstract:
In this paper , we study the existence of a weak solutions for the
initial-boundary value problems of the strongly nonlinear degenerated parabolic
equation,
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*)).
∂u
+A(u)+g(x,t,u,∇ u)=f
∂t
Paper's Title:
Renormalized Solutions for Nonlinear Parabolic Equation with Lower Order Terms
Author(s):
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,
Morocco.
2Faculté des Sciences
Juridiques, Economiques et Sociales,
Université Hassan 1, B.P. 784. Settat,
Morocco.
aberqiahmed@ya_hoo.fr
jbennouna@hotmail.com
mekkour.mounir@yahoo.fr
redwane_hicham@yahoo.fr
Abstract:
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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