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.

Paper's Title:

Existence and Regularity of Minima of an Integral Functional in Unbounded Domain

Author(s):

L. Aharouch, J. Bennouna and A. Bouajaja

King Khalid University
Faculty of Arts and Science Mha'l Asir
Saudi Arabia.

E-mail: laharouch@gmail.com

Université Sidi Mohammed Ben Abdellah
Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fès,
Maroc.

Email: jbennouna@hotmail.com

E-mail: kadabouajaja@hotmail.com

Abstract:

We prove the existence and the regularity of minima for a functional defined on a suitable Sobolev space.

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