Existence and stability in the α-norm for nonlinear neutral partial differential equations with finite delay

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DOI:

https://doi.org/10.4067/S0719-06462013000100004

Abstract

In this work, we study the existence, regularity and stability of solutions for some nonlinear class of partial neutral functional differential equations. We assume that the linear part generates a compact analytic semigroup on a Banach space X, the delayed part is assumed to be continuous with respect to the fractional power of the generator. For illustration, some application is provided for some model with diffusion and nonlinearity in the gradient.

Keywords

Neutal equation , Analytic semigroup , Fractional power , Mild solution , Strict solution
  • Taoufik Chitioui Université de Sfax, Faculté des Sciences de Sfax, Sfax, Tunisie.
  • Khalil Ezzinbi Caddy Ayyad University, Université Cadi Ayyad, Faculté des Sciences Semlalia, BP 2390, Marrakech, Morocco.
  • Amor Rebey Université de Kairouan Institut Supérieur des Mathématiques Appliquées et de l‘Informatique, Tunisie.
  • Pages: 49–75
  • Date Published: 2013-03-01
  • Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal

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Published

2013-03-01

How to Cite

[1]
T. Chitioui, K. Ezzinbi, and A. Rebey, “Existence and stability in the α-norm for nonlinear neutral partial differential equations with finite delay”, CUBO, vol. 15, no. 1, pp. 49–75, Mar. 2013.