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Zbl 1197.35072
Sun, Chunyou
Asymptotic regularity for some dissipative equations. (English)
[J] J. Differ. Equations 248, No. 2, 342-362 (2010). ISSN 0022-0396

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.
[Bixiang Wang (Socorro)]

MSC 2000:: *35B65 Smoothness of solutions of PDE
35B41 Attractors
35K57 Reaction-diffusion equations
35L05 Wave equation
35B40 Asymptotic behavior of solutions of PDE

Keywords: asymptotic regularity; reaction-diffusion equation; wave equation; attractor; diffusion equation with polynomially growing nonlinearity; damped wave equation with critical nonlinearity

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Zentralblatt MATH Berlin [Germany]