The Existence Of For N-dimensional Nonlinear Evolution Equations (Systems) Of Higher Order And Vacuum Isolating Property

The first chapter introduces the background of the problem.In the second chapter, the existence and uniqueness of the global strong solution have been studied by using Galerkin method for a class of n-dimensional Nonlinear evolution equation systems of higher order(2.1)--(2.3).In the third chapter, a class of n-dimensional Nonlinear evolution equation of higher order(3.1)—(3.3) have been studied by the method of potential wells. The existence and uniqueness of the global strong solution have been proved.In the fourth chapter, based on the existence of the global strong solution in problem(3.1)--(3.3),vacuum isolating property of the solutions of the following n-dimensional nonlinear evolution equation is gained by using a family of the potential wells.