The Existence Of Solutions For Multidimensional Viscoelasticity Equation

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.