The Dynamics Of Solutions For Generalized Kirchhoff And Boussinesq Equations

One of the aims of this study is to develop the well-posedness andthe uniform decay rate of energy for coupled wave equations of Kirchhoff typewith nonlinear boundary damping and memory source term. For the dampedKirchhoff equation, the oscillation solution has been found to be decaiedexponentially in time as t→∞.Secondly, based on the study of viscous Boussinesq equations, a num-ber of theorems for the existence and uniqueness of solutions to initialvalue problem associated with the equations have been developed. Theresults from the analysis of viscous Boussinesq equations investigated in chapter3 has extended the corresponding theorems in Y. Thomas and Li. Congming [13].