On Nonlinear Wava Equation With Dynamical Boundary Conditions,Interior Degenerate Damping And Source

In this article,we focus on the initial-boundary value problem of nonlinear wave equation with dynamical boundary conditions,interior degenerate damping and source(?) where ? is a open bounded subset of RN(N?2)with C1 boundary,?=(?)?,(?0,?1)is a measurable partition of ?,?? denotes the Laplace-Beltrami operator on ?,v is the outward normal to ?,(?)j is a sub-differential of a continuous convex function j,|(?)j(s)|?c0|s|m+c2(c0>0,c2?0),with some conditions on j and the parameters in the equations.By means of Galerkin method and Kakutani-type theorem,under nominal assumptions on the parameters we establish the existence of locally generalized solutions.When p ?k+m,the solution is global.With further restrictions on the exponents we prove the existence and uniqueness of a global weak solution.In addition,we obtain blow-up results of weak solutions when p>m+k and the initial energy is negative.