【作者】 李金蔚；

【导师】 蒲志林；

【作者基本信息】 四川师范大学 ， 运筹学与控制论， 2011， 硕士

【摘要】 本文运用了Potential Well方法研究了一类强阻尼波动方程组初边值问题在Rn整体解的存在性,定义了该方程组的位势深度d,运用庞加莱-索伯列夫嵌入定理证明了位势深度d>0,再通过构建适当的能量函数E(t),稳定集和不稳定集,当初始值属于不稳定集时,解在有限时间爆破和解的衰减估计.第一章介绍了预备知识.第二章讨论了一类强阻尼波动方程组初边值问题在Rn解的存在性.第三章研究了一类强阻尼波动方程组初边值问题在Rn解的爆破,第四章介绍了一类强阻尼波动方程组初边值问题在Rn解的一致衰减估计.更多还原

【Abstract】 The global existence of solution for a class of strongly damped wave equations with initial-boundary value problem is studied using Potential Well method. The Potential depth of this problem are defined,and by using Poincare-Sobolev embedding theorem, it is proved that the potential depth is a positive number. The paper introductes the energy function,the stable and unstable sets,we prove that the existence of global solutions under some conditions.it is also show that if the initial data belongs to the unstable set,the solution is blowed up in finite time,the decay behavior of solution is disscussed.In chapter one,We introduce basic knowledge;In chapter two,We introduce the global existence of solution for the strongly damped wave equations with initial-boundary value problem is studied.In chapter three,We introduce the global blow up of solution for the strongly damped wave equations with initial-boundary value problem is studied.In chapter four,We introduce the decay behavior of solution for the strongly damped wave equations with initial-boundary value problem is studied.更多还原