Structure of the pullback attractorfor a non-autonomous scalar differential inclusion

T.  Caraballo; J. A.  Langa; J.  Valero

doi:10.3934/dcdss.2016037

Article Contents

2016, Volume 9, Issue 4: 979-994. Doi: 10.3934/dcdss.2016037

This issue Previous Article Recurrent equations with sign and Fredholm alternative Next Article On integral separation of bounded linear random differential equations

Structure of the pullback attractor for a non-autonomous scalar differential inclusion

1.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad, s/n, 03202-Elche

Received: September 2015

Revised: January 2016

Published online: August 2016

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Abstract

The structure of attractors for differential equations is one of the main topics in the qualitative theory of dynamical systems. However, the theory is still in its infancy in the case of multivalued dynamical systems. In this paper we study in detail the structure and internal dynamics of a scalar differential equation, both in the autonomous and non-autonomous cases. To this aim, we will also show a general result on the characterization of a pullback attractor for a multivalued process by the union of all the complete bounded trajectories of the system.

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Mathematics Subject Classification: 35B40, 35B41, 34C37, 34D45.

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