The Existence Of Time-dependent Attractor For Fractional Damping Wave Equations

In recent years,M.Conti,F.Di Plinio and other scholars introduced the concept of time-dependent global attractors and applied them into the wave equations and oscillation equations,respectively.Based on these latest abstract results,the time-dependent asymptotic behavior of the fractional damped wave equation has been studied in two parts in this paper.First,by combining with the methods and tech-niques of Yang Zhijian et.al in[10,15],we obtain the continuity and compactness of the family process for the corresponding problem,then achieve,the existence and regularity as well as the upper semi-continuity of the time-dependent attractor of the fractional damped wave equation.Second,applying the method of asymptotically compactness of the family process established by Meng Fengjuan etc.in[13],name-ly,by the method of contraction function,we prove the existence of time-dependent attractors for damped wave equation with linear memory.