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Asymptotic regularity for some dissipative equations. (English) Zbl 1197.35072
Author’s abstract: This paper is devoted to proving some asymptotic regularity, for both reaction-diffusion equation with a polynomially growing nonlinearity of arbitrary order and strongly damped wave equation with critical nonlinearity, which excel the sharp regularity allowed by the corresponding stationary equations (equilibrium points). Based on this regularity, the existence of the finite-dimensional global and exponential attractors can be obtained easily.

35B65Smoothness and regularity of solutions of PDE
35B41Attractors (PDE)
35K57Reaction-diffusion equations
35L05Wave equation (hyperbolic PDE)
35B40Asymptotic behavior of solutions of PDE
Full Text: DOI
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