The Studies On Damped Wave Equation With Dynamic Boundary Conditions

In this paper, the existence of solutions, the asymptotic behavior of global solutions and the nonexistence of global solutions for the following initial boundary value problem of wave equation with damped are discussed, where p, α,β,δ are positive constants and p≥2, g(s)=|s|P-2s.By using Galerkin method and the contractive mapping principle, we prove the existence of local solutions for problem (1-1)-(1-4). When f=0, introducing the potential well theory, the energy decay of the global solutions are proposed with the help of Nakao’s inequality. By using the classical convexity lemma, the sufficient conditions of the nonexistence of global solutions of the wave equation with negative and positive initial energy are obtained, respectively. When f≠0, with the help of a comparison inequality, we obtain the relationship between the energy decay of the problem (1-1)-(1-4) and the term of external force.