LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N  

作　　者：Azer KHANMAMEDOV Sema YAYLA Azer KHANMAMEDOV;Sema YAYLA(Department of Mathematics, Faculty of Science, Hacettepe University)

机构地区：Department of Mathematics,Faculty of Science,Hacettepe Universit

出　　处：《Acta Mathematica Scientia》2018年第3期1025-1042,共18页数学物理学报（B辑英文版）

基　　金：supported by Research Fund of the Hacettepe University.Project Number:FBB-2017-16218

摘　　要：We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in R^n, then the semigroup generated by the considered problem possesses a global attractor in H^2（R^n） × L^2（R^n）.We also establish the boundedness of this attractor in H^3（R^n） × H^2（R^n）.We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in R^n, then the semigroup generated by the considered problem possesses a global attractor in H^2（R^n） × L^2（R^n）.We also establish the boundedness of this attractor in H^3（R^n） × H^2（R^n）.

关 键 词：Wave equation plate equation global attractor 

分 类 号：O175[理学—数学]