The Global Attractors Of Nonlinear Wave Equations With A Memory

In nature, many natural phenomena can be study by partial differential equations, and many dynamic phenomena be affected by one or more variables of the past history.It is here considered wave equations containing a memory term.It is also accounted for that some people's work and the mathematical methods and the main results they have obtain in recent years,especially for the existence of global solution and global attractors.In this paper, we will make research about the global attractor existence of the damped wave equation with a memory term by means of operator semigroups theory,under the boundary conditions and the initial conditions whereΩis a bounded domain in Rn with smooth boundary,α> 0.The details will go as follows:Firstly, the paper introduces the current domestic and international research situation and direction of the wave equation with a memory term briefly;Secondly, we put forward some important definitions and lemmas,and briefly explain some marks;Thirdly, we prove the existence and uniqueness of the global solution for system (1.2.1)-(1.2.3) by means of the Faedo-Garlerkin method; Fourthly, we prove the existence of the global attractor for solution semigroups;Fifthly, we make some prospects of the evolution equation with a nonlinear memory term research in the future.