Convergence Rate of Solutions to a Hyperbolic Equation with p(x)-Laplacian Operator and Non-Autonomous Damping  

作　　者：Wenjie Gao Xiaolei Li Chunpeng Wang 

机构地区：[1]School of Mathematics,Jilin University,Changchun,Jilin 130012,P.R.China

出　　处：《Communications in Mathematical Research》2023年第2期190-208,共19页数学研究通讯（英文版）

基　　金：The research was supported by the National Key R&D Program of China(Grant No.2020YFA0714101);by the National Natural Science Foundation of China(Grant No.11925105);by the Graduate Innovation Fund of jilin University.

摘　　要：This paper concerns the convergence rate of solutions to a hyperbolic equation with p(x)-Laplacian operator and non-autonomous damping.We apply the Faedo-Galerkin method to establish the existence of global solutions,and then use some ideas from the study of second order dynamical system to get the strong convergence relationship between the global solutions and the steady solution.Some differential inequality arguments and a new Lyapunov functional are proved to show the explicit convergence rate of the trajectories.

关 键 词：Convergence rate energy estimate non-autonomous damping 

分 类 号：O175.8[理学—数学]