An extension of the concept of gradient semigroups which is stable under perturbation


Autoria(s): CARVALHO, Alexandre N.; LANGA, Jose A.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

20/10/2012

20/10/2012

2009

Resumo

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

Identificador

JOURNAL OF DIFFERENTIAL EQUATIONS, v.246, n.7, p.2646-2668, 2009

0022-0396

http://producao.usp.br/handle/BDPI/28852

10.1016/j.jde.2009.01.007

http://dx.doi.org/10.1016/j.jde.2009.01.007

Idioma(s)

eng

Publicador

ACADEMIC PRESS INC ELSEVIER SCIENCE

Relação

Journal of Differential Equations

Direitos

restrictedAccess

Copyright ACADEMIC PRESS INC ELSEVIER SCIENCE

Palavras-Chave #DIFFERENTIAL-EQUATIONS #ATTRACTORS #EXISTENCE #Mathematics
Tipo

article

original article

publishedVersion