Study On The Properties Of Solutions For Two Classes Wave Equation(s)

PDEs have been widely applied in the disciplines of physics,chemistry and so on.As one of the most important PDEs,the wave equation describes all kinds of waves and appears in various filed,for example,acoustics,electromagnetics and fluid mechanics.Therefore,the study for wave equations has important significance in both theoretical and practical sense.However,most of the nonlinear wave equations,which stem from practical problems and are quite difficult to solve.It has been a challenging task for mathematicians and physicists to study the existence and other properties of solutions to the nonlinear wave equations.In this thesis,we study the global existence,decay and blow-up of solutions for two classes of nonlinear wave equations and systems with damping and source terms.First of all,we discuss the following coupled nonlinear wave equations with initialboundary value conditions and strong damping,frictional damping and source terms,By using the multiplier method and Nakao’s inequality,we give the results of the global existence and the decay estimates.We also prove the blow-up of the solution in finite time by using the perturbed energy method.Secondly,we discuss the following wave equations with initial-boundary value conditions and Balakrishnan-Taylor damping,viscoelastic damping,history memories and source terms,By using the multiplier method and the perturbed energy method,we give the results of the global existence and the general energy decay.