Abstract
In this paper we study the existence of global compact attractors for nonlinear parabolic equations of the reaction-diffusion type and variational inequalities. The studied equations are generated by a difference of subdifferential maps and are not assumed to have a unique solution for each initial state. Applications are given to inclusions modeling combustion in porous media and processes of transmission of electrical impulses in nerve axons.
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Valero, J. Attractors of Parabolic Equations Without Uniqueness. Journal of Dynamics and Differential Equations 13, 711–744 (2001). https://doi.org/10.1023/A:1016642525800
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DOI: https://doi.org/10.1023/A:1016642525800