Decay Rate Of Wave Equations With Boundary Memory Damping

Partial differential equation is a very important branch discipline in the field of mathematics,and wave equation is an important component of partial differential equation.With the development of science and technology,it is found that wave equation is more and more closely connected with other disciplines,especially in physics,biology,finance and other disciplines.Most literatures study the blow-up of wave equation solution,boundary controllability and its feedback stabilization.However,There is little research on acoustic wave equations.Therefore,this paper mainly qualitatively analyzes the polynomial attenuation of semi-linear acoustic wave equations with boundary memory damping and the general attenuation of wave equations with nonlinear acoustic boundary conditions.In the first chapter,the development of acoustic wave equation is briefly described,then the research status of related problems of acoustic wave equation with different boundaries is written,and finally the research status of damped wave equation with boundary memory is briefly described.In the second chapter,a semi-linear wave equation with boundary memory damping is discussed.Firstly,the multiplier method is applied to establish the corresponding energy function.Then,the energy function can be simply deformed to prove the well-posedness of the solution.Then,a theorem on attenuation is obtained.Through order reduction of the system,Lyapunov function is established to prove that the energy of the wave equation with boundary memory damping is polynomial attenuated.In the third chapter,the general attenuation of wave equation with nonlinear acoustic boundary condition with boundary memory damping is studied.Firstly,the corresponding energy function is established.Then,the multiplier method is used to deal with each term in the energy functional.Finally,the energy function satisfies the corresponding differential equation and condition to prove the general attenuation of the system.