On a class of nonlinear anisotropic parabolic problems

M. H. Abdou; M. Chrif; S. El Manouni; H. Hjiaj

doi:10.1017/S0308210515000402

On a class of nonlinear anisotropic parabolic problems

Part of: Parabolic equations and systems Elastic materials

Published online by Cambridge University Press: 22 October 2015

M. H. Abdou ,

M. Chrif ,

S. El Manouni and

H. Hjiaj

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M. H. Abdou: Affiliation:
Département de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796 Fés-Atlas, 30003 Morocco (mohamedhousseine@yahoo.fr)
M. Chrif: Affiliation:
Département de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796 Fés-Atlas, 30003 Morocco (moussachrif@yahoo.fr)
S. El Manouni: Affiliation:
Department of Mathematics, Faculty of Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), PO Box 90950, Riyadh 11623, Saudi Arabia (samanouni@imamu.edu.sa)
H. Hjiaj: Affiliation:
Département de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796 Fés-Atlas, 30003 Morocco (hjiajhassane@yahoo.fr)

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Abstract

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Abstract

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We prove the existence of weak solutions for the strongly nonlinear parabolic problem

in the anisotropic Sobolev space , where the data f are assumed to be in the dual, and the nonlinear term g(x, t, s) has growth and sign conditions on s.