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On a class of nonlinear anisotropic parabolic problems

Part of: Elastic materials Parabolic equations and systems

Published online by Cambridge University Press:  22 October 2015

M. H. Abdou ,
M. Chrif ,
S. El Manouni  and
H. Hjiaj
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

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.

Keywords

anisotropic Sobolev spacestrongly nonlinear parabolic problemsweak solution

MSC classification

Primary: 35K55: Nonlinear parabolic equations 74B20: Nonlinear elasticity 35K58: Semilinear parabolic equations 35K59: Quasilinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 1 , February 2016 , pp. 1 - 21
Copyright
Copyright © Royal Society of Edinburgh 2016 

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