# American Institute of Mathematical Sciences

August  2016, 9(4): 979-994. doi: 10.3934/dcdss.2016037

## 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, Spain, Spain 2 Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad, s/n, 03202-Elche, Spain

Received  September 2015 Revised  January 2016 Published  August 2016

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.
Citation: T. Caraballo, J. A. Langa, J. Valero. Structure of the pullback attractor for a non-autonomous scalar differential inclusion. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 979-994. doi: 10.3934/dcdss.2016037
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