The Properties Of Global Solution For Three Kinds Of Non-linear Wave Systems

This paper deals with some properties of solution to three typesof partial di-erent equations. In chapter 2, we aim at the studyof initial boundary problem for the scattering Boussinesq equationutt - auttxx - 2butxx + mut = -cuxxxx + uxx - p2u +β(u2)xx. The well-posedness of global solution and the long time asymptotic behavior of the formalapproximation solution to this type equation is discussed in detail in a classicalspace by using perturbation method.In chapter 3, we study the initial value problem of the semi-linearwave eqution utt - uxx - muttxx + bu =εf(t,x,u,ε). In a Sobolev spaceC JL,Hs(R) C1 JL,Hs-1(R) , we obtain the existence and uniqueness ofthe solution by the means of the Banach fixed-point theory and get the formalapproximation solution of it.In chapter 4, we discuss the initial value problem of the semi-lineartelegraph equation utt - uxx + put + qu = f(u). The existence and unique-ness of global solution of the question are established in a Sobolev spaceC([0,∞), Hs+1(R))∩C1([0,∞), Hs(R)). We confirm the fact that the longtime stability of the emission wave is partly in-uenced by the initial input signal.