【作者】 黄文毅；

【导师】 赖绍永；

【作者基本信息】 四川师范大学 ， 基础数学， 2006， 硕士

【摘要】 本文的研究工作之一是:对具有非线性边界阻尼和记忆源项的Kirchhoff型对偶波系统,得到了其解适定性及能量的一致衰减估计;当t→∞时,指出了阻尼Kirchhoff型方程的振动解呈现指数衰减.其二,本文研究了粘性Boussinesq方程,建立了该系统初值问题解的存在性和唯一性定理.在第三章中,得到了粘性Boussinesq系统的一些新结果,推广了Y. Thomas和Li. Congming文[13]中的相应结论.更多还原

【Abstract】 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].更多还原