Global Existence And Blow-up For A Class Of Sixth-order Hyperbolic Equation

In this thesis,we consider the initial-boundary value problem for a class of sixth-order hyperbolic equation(?) where ??Rn is a bounded domain with a smooth boundary ?Q,?>2,?>1,p satisfy(?)In this thesis,we investigate some properties of solutions for the sixth order hyperbolic equation at three different initial energy levels.First we prove the local existence of weak solution by Galerkin method and contraction mapping principle.Moreover by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions,but also give some threshold results of global existence of solutions.Also we discuss the global existence of solutions for problem with critical and sub-critical initial conditions.Finally the blow up of solutions for problem with initial conditions are proved.