Some Problems For N-dimensional Nonlinear Pseudo-hyperbolic Equation(System) Of Higher Order

In the second part of the paper, the initial boundary value problems for a class of n-dimensional nonlinear pseudo-hyperbolic system of higher order(2.1)--(2.4) have been studied by Galerkin method, combining with the priori estimate of solution and Sobolev imbedding theorems. The existence and uniqueness of the global strong solution have been proved,In the third part of the paper, the initial boundary value problems for a class of n-dimensional nonlinear pseudo-hyperbolic 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 part of the paper, based on existence of the solution of the problem (3.1)--(3.3),vacuum isolating property of the solutions of the following n-dimensional nonlinear pseudo-hyperbolic equation is gained by using the family of new potential wells which is defined in this paper,...