The Stady Of Solution For Strongly Damped Wave Equations

The global existence of solution for a class of strongly damped wave equations with initial-boundary value problem is studied using Potential Well method. The Potential depth of this problem are defined,and by using Poincare-Sobolev embedding theorem, it is proved that the potential depth is a positive number. The paper introductes the energy function,the stable and unstable sets,we prove that the existence of global solutions under some conditions.it is also show that if the initial data belongs to the unstable set,the solution is blowed up in finite time,the decay behavior of solution is disscussed.In chapter one,We introduce basic knowledge;In chapter two,We introduce the global existence of solution for the strongly damped wave equations with initial-boundary value problem is studied.In chapter three,We introduce the global blow up of solution for the strongly damped wave equations with initial-boundary value problem is studied.In chapter four,We introduce the decay behavior of solution for the strongly damped wave equations with initial-boundary value problem is studied.