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

被引：13

作者：

Adimy, Mostafa

Ezzinbi, Khalil

机构：

[1] Univ Pau, Lab Math Appl, IPRA, FRE 2570, F-64000 Pau, France

[2] Univ Cadi Ayyad, Dept Math, Fac Sci Semlalia, Marrakech, Morocco

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2006年 / 185卷 / 03期

关键词：

partial functional differential equations; analytic semigroup; fractional power; mild solution; characteristic value; stability;

D O I：

10.1007/s10231-005-0162-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 a-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 (199 1), 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)).

引用

页码：437 / 460

页数：24

共 18 条

[1] A class of linear partial neutral functional differential equations with nondense domain [J].