Time-Dependent Asymptotic Behavior Of Wave Equations With Strong Damping Or Linear Memory On R~n

For the past few years,Conti M,Plinio Di F et al.proposed a new notion of time-dependent global attractor when studying the oscillation equation and wave equation with time-dependent coefficients,and in dissipative partial differential equations,a method is provided to testify the existence of time-dependent global attractors.To certify the existence of this attractor,compactness verification of the solution process is necessary.In 2019,Liu T T,Ma Q Z established a compression function method for proving the compactness of solution processes related to dissipative partial differential equations on unbounded domain.Based on this abstract theory,in this thesis the time-dependent asymptotic properties of wave equations with strong damping or linear memory are studied in two parts by using the ways of asymptotic prior estimation,tail estimation,condition(Ct)and compression function.The first part,we talk about the time-dependent attractors of wave equations with strong damping on Rn.Firstly,we testify the existence of time-dependent absorption set by a priori estimation.Secondly,the proof of compactness on Rn is more complex,we use the method of tail estimate,by a method of condition(Ct)to verifying ?t-limit compact to obtain that the process is asymptotically compact.and then the existence of time-dependent attractors is obtained.The second part.we investigate the time-dependent attractors of wave equations with linear memory on Rn.Firstiy,we have the existence of the absorption set.Secondly,we verify the process is asymptotically compact by using the tail estimate and compression function way,and the existence of time-dependent attractors is obtained.