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 Ω is a open bounded subset of RN(N≥2)with C1 boundary,Γ=(?)Ω,(Γ0,Γ1)is a measurable partition of Γ,△Γ denotes the Laplace-Beltrami operator on Γ,v is the outward normal to Ω,(?)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.