Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 62, No. 2, pp. 143-183 (2005)

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Strongly nonlinear parabolic equations with natural growth terms and $L^{1}$ data in Orlicz spaces

A. Elmahi and D. Meskine

C.P.R., B.P. 49,
E-mail: elmahi_abdelhak@yahoo.fr
Département de Mathématiques et Informatique,
Faculté des Sciences Dhar Mahraz, B.P. 1796 Atlas, Fès -- MOROCCO
E-mail: meskinedriss@hotmail.com

Abstract: We prove compactness and approximation results in inhomogeneous Orlicz--Sobolev spaces and look at, as an application, the Cauchy--Dirichlet problem $u^{\prime}+A(u)+g(x,t,u,\nabla u)=f\in L^{1}$. We also give a trace result allowing to deduce the continuity of the solutions with respect to time.

Keywords: inhomogeneous Orlicz--Sobolev spaces; parabolic problems; lack of compactness; approximation.

Classification (MSC2000): 35K15, 35K20, 35K60.

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Electronic version published on: 7 Mar 2008.

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