Annali di Matematica Pura ed Applicata

, Volume 185, Issue 3, pp 437–460

Existence and stability in the α-norm for partial functional differential equations of neutral type

Article

DOI: 10.1007/s10231-005-0162-8

Cite this article as:
Adimy, M. & Ezzinbi, K. Annali di Matematica (2006) 185: 437. doi:10.1007/s10231-005-0162-8

Abstract

In this work, we study a general class of partial neutral functional differential equations. We assume that the linear part generates an analytic semigroup and the nonlinear part is Lipschitz continuous with respect to the é-norm associated to the linear part. We discuss the existence, uniqueness, regularity and stability of solutions. Our results are illustrated by an example. This work extends previous results on partial functional differential equations (Fitzgibbon and Parrot, Nonlinear Anal., TMA 16, 479–487 (1991), Hale, Rev. Roum. Math. Pures Appl. 39, 339–344 (1994), Hale, Resen. Inst. Mat. Estat. Univ. Sao Paulo 1, 441–457 (1994), Travis and Webb, Trans. Am. Math. Soc. 240 129–143 (1978), Wu and Xia, J. Differ. Equ. 124 247–278 (1996)).

Keywords

Partial functional differential equationsAnalytic semigroupFractional powerMild solutionCharacteristic valueStability

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées, I.P.R.A., FRE 2570Université de Pau, Avenue de l’universitéPauFrance
  2. 2.Département de Mathématiques, Faculté des Sciences SemlaliaUniversité Cadi AyyadMarrakeshMorocco