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Trajectory and global attractors for generalized processes

Dedicated to Peter Kloeden on occasion if his 70th birthday

This research was partially supported by Programa Ciência sem Fronteiras/CNPq process 200493/2015-9 and CNPq process 140943/2013-7, Ministério da Ciência e Tecnologia, Brazil, by FEDER and Ministerio de Economía y Competitividad under grant MTM2015-63723-P and Junta de Andalucía under Proyecto de Excelencia P12-FQM-1492

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  • In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem and, through this approach, some conditions for the existence of trajectory attractors are proved. By projecting the trajectory attractor on the phase space, the uniform attractor for the multivalued process associated to the problem is obtained and some conditions to guarantee the invariance of the uniform attractor are given. Furthermore, the existence of the uniform attractor for a class of $ p $-Laplacian non-autonomous problems with dynamical boundary conditions is established.

    Mathematics Subject Classification: 35B40, 35B41, 35K55, 37B55.


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