PORTUGALIAEMATHEMATICA
Vol. 62, No. 2, pp. 143-183 (2005)
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PORTUGALIAE MATHEMATICA 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 spacesA. Elmahi and D. MeskineC.P.R., B.P. 49,Fès -- MOROCCO 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. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2005 Sociedade Portuguesa de Matemática
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