Finite Time Blow Up And Decay Estimates Of Solution For A Class Of Fourth Order Nonlinear Wave Equation

Let Ω(?)RN RN be a bounded domain with smooth boundary (?)Ω. The following problem with nonlinear damping and source term was considered, Where m> 1, p> 1 and △ is Laplacian in RN. Firstly, the local existence and uniqueness for the problem is established. Furthermore, the blow up of this solution is obtained. In addition, if the data belongs to the stable set, the global existence and decay estimates of solution are studied. The main contents of this thesis are summarized as follows.In Chapter one, the historical background and some basic facts for wave equation with nonlinear damping and source term are introduced respectively.In Chapter two, by the fixed point theory, the local existence and uniqueness for solution of the problem is proved.In Chapter three, the blow-up of the solution is proved provided that on m<p and E(0)< 0 introducing a blowing up factor, Moreover the upper bound for the lifespan of the solution is give.In Chapter four, two global existence results are obtained. Firstly, with the presence of t0 such that E(to)<d and the data belongs to the stable set, the global existence and decay estimates of solution are proved regardless of any relations between m and p. Furthermore, if m≥p, the solution is global as well.