【作者】 马慧；

【导师】 刘亚成；

【作者基本信息】 哈尔滨工程大学 ， 应用数学， 2007， 硕士

【摘要】 本文分别用Galerkin法和位势井法研究了以下多维粘弹性方程在正定能量下和非正定能量下的初边值问题整体解的存在性，其中Q表示区间(0，1)(对初边值问题及周期边界问题)或(-∞，∞)(对初值问题)。同时，对正定能量下的周期边界问题及初值问题也进行了研究，并在σ(s)∈C~1，σ(s)下方有界的条件下，得到了整体强解的存在和唯一性，而在其初值函数满足一定的光滑性条件下，得到强解的相应光滑性，对非正定能量下我们得到了解的真空隔离现象。更多还原

【Abstract】 In this paper, multidimensional viscoelasticity equation is considered by Galerkin method and potential well under positive energy and nonpositive energy .WhereΩbelongs to (0,1) if it is initial boundary walue problem and periodic boundary problem or (-∞,∞) if it is initial value problem. And the existence of global solutions are established.At the same time, periodic boundary problem and initial value problem of equation under positive energy are studied .Under the conditions ofσ(s)∈C~1,σ’(s) bounded below, we prove the existence and uniqueness of the global strong solutions. While the inatial value function smooth appropriate, we obtain the smooth theorems of the global strong solutions. Behaviour of vacuum isolating of solutions is studied under nonpositive enegy.更多还原