The Decaying Properties Of Solutions For Two Types Of Boussinesq Systems

This paper deals with two types of Boussinesq equation with ini-tial boundary conditions. The existence and uniform decay of solutions for thetwo kinds of wave equations will be established under the assumptions of initialboundary data.In chapter one, some backgrounds of recent study for Boussinesq systemsare briefly introduced.In chapter two, the following damped Boussinesq system with initial-boundary conditions in one-dimensional space is considerdwhere a＞0, b, c andεare positive constants, h andβ∈R¹.Under some assumptions, the well-posedness of solution for equation (0-1) isestablished. It is proved that the long time behavior of the solution shows thepresence of damped oscillations decaying exponentially in time as t→∞.In chapter three, the decaying properties of solutions for the following prob- lem are developedwhere a₁, a₂, b₁, b₂, c₁, c₂, d₁, d₂ are positive numbers, and h,β₁,β₂∈R¹.The perturbation technique will be used to discuss the properties of solutionsfor problem (0-2). Its exact solution is constructed in the form of a series in asmall parameter provided in the initial conditions. The long-time asymptoticsof the solution is shown to decay exponentially in time.The mathematical technique used in this paper is mainly refered to [14].However, the Boussinesq systems investigated are different from those inprevious works [13], [14], [15], [16].