Skew-product semiflows for non-autonomous partial functional differential equations with delay

Sylvia Novo; Carmen Núñez; Rafael Obaya; Ana M. Sanz

doi:10.3934/dcds.2014.34.4291

Article Contents

2014, Volume 34, Issue 10: 4291-4321. Doi: 10.3934/dcds.2014.34.4291

This issue Previous Article The Penrose-Fife phase-field model with coupled dynamic boundary conditions Next Article The existence and decay estimates of the solutions to $3$D stochastic Navier-Stokes equations with additive noise in an exterior domain

Skew-product semiflows for non-autonomous partial functional differential equations with delay

1.
Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid
2.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 47011 Valladolid
3.
Departamento de Didáctica de las Ciencias Experimentales, Sociales y de la Matemática, E.U. Educación, Universidad de Valladolid, 34004 Palencia

Received: December 31, 2012

Revised: February 28, 2013

Published: September 2014

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Abstract

A detailed dynamical study of the skew-product semiflows induced by families of AFDEs with infinite delay on a Banach space is carried over. Applications are given for families of non-autonomous quasimonotone reaction-diffusion PFDEs with delay in the nonlinear reaction terms, both with finite and infinite delay. In this monotone setting, relations among the classical concepts of sub and super solutions and the dynamical concept of semi-equilibria are established, and some results on the existence of minimal semiflows with a particular dynamical structure are derived.

Keywords:

Topological dynamics,
skew-product semiflows,
abstract functional differential equations,
partial functional differential equations,
finite delay,
infinite delay.

Mathematics Subject Classification: 37B55, 37C69, 37K57, 35R10.

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