American Institute of Mathematical Sciences

May  2015, 20(3): 781-810. doi: 10.3934/dcdsb.2015.20.781

Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces

 1 Department of Mathematics, University of Surrey, Guildford, GU2 7XH

Received  April 2014 Revised  August 2014 Published  January 2015

We give a comprehensive study of strong uniform attractors of nonautonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces that are not translation compact, but nevertheless allow the attraction in a strong topology of the phase space to be verified and discuss in a more detailed way the class of so-called normal external forces introduced before. We also develop a unified approach to verify the asymptotic compactness for such systems based on the energy method and apply it to a number of equations of mathematical physics including the Navier-Stokes equations, damped wave equations and reaction-diffusing equations in unbounded domains.
Citation: Sergey Zelik. Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 781-810. doi: 10.3934/dcdsb.2015.20.781
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