Mostafa Adimy, Mohamed Alia, Khalil Ezzinbi
Abstract:
We study the existence, regularity and stability of solutions for nonlinear
partial neutral functional differential equations with unbounded delay
and a Hille-Yosida operator on a Banach space X.
We consider two nonlinear perturbations: the first one is a function taking
its values in X and the second one is a function belonging to a space
larger than X, an extrapolated space. We use the extrapolation techniques
to prove the existence and regularity of solutions and we establish a
linearization principle for the stability of the equilibria of our equation.
Submitted May 10, 2013. Published August 25, 2014.
Math Subject Classifications: 35R10, 47D06.
Key Words: Neutral differential equation; infinite delay; extrapolation space;
mild solution; semigroup; stability.
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Mostafa Adimy INRIA Rhône-Alpes, Université Lyon 1 Institut Camille Jordan, 43 Bd. du 11 novembre 1918 F-69200 Villeurbanne Cedex, France email: mostafa.adimy@inria.fr |
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Mohamed Alia Université Cadi Ayyad, Faculté des Sciences Semlalia Département de Mathématiques BP. 2390, Marrakesh, Morocco email: monsieuralia@yahoo.fr |
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Khalil Ezzinbi Université Cadi Ayyad, Faculté des Sciences Semlalia Département de Mathématiques BP. 2390, Marrakesh, Morocco email: ezzinbi@ucam.ac.ma |
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