Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

The uniform attractor of a multi-valued process generated by reaction-diffusion delay equations on an unbounded domain

Pages: 4343 - 4370, Volume 34, Issue 10, October 2014      doi:10.3934/dcds.2014.34.4343

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Yejuan Wang - School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China (email)
Peter E. Kloeden - Institut für Mathematik, Goethe Universität, D-60054 Frankfurt am Main, Germany (email)

Abstract: The existence of a uniform attractor in a space of higher regularity is proved for the multi-valued process associated with the nonautonomous reaction-diffusion equation on an unbounded domain with delays for which the uniqueness of solutions need not hold. A new method for checking the asymptotical upper-semicompactness of the solutions is used.

Keywords:  Multi-valued process, uniform attractor, asymptotical upper-semicompactness, reaction-diffusion equation with delay.
Mathematics Subject Classification:  Primary: 35R10, 35B41; Secondary: 47H20.

Received: May 2012;      Revised: October 2012;      Available Online: April 2014.