Open AccessAsymptotics of singularly perturbed damped wave equations with super-cubic exponent
Author(s) -
Dandan Li
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021056
Subject(s) - attractor , bounded function , mathematics , mathematical analysis , domain (mathematical analysis) , extension (predicate logic) , nonlinear system , limit (mathematics) , class (philosophy) , parabolic partial differential equation , hyperbolic partial differential equation , exponent , partial differential equation , physics , linguistics , quantum mechanics , artificial intelligence , computer science , programming language , philosophy
This work is devoted to studying the relations between the asymptotic behavior for a class of hyperbolic equations with super-cubic nonlinearity and a class of heat equations, where the problem is considered in a smooth bounded three dimensional domain. Based on the extension of the Strichartz estimates to the case of bounded domain, we show the regularity of the pullback, uniform, and cocycle attractors for the non-autonomous dynamical system given by hyperbolic equation. Then we prove that all types of non-autonomous attractors converge, upper semicontiously, to the natural extension global attractor of the limit parabolic equations.