The Initial Boundary Value Problem Of The Double Dispersion Wave Equation With Nonlinear Damping Term

In this thesis, we investigate the initial-boundary value problem of double dispersion wave equation with nonlinear damping term utt — △utt —△ u + △2u — △g(ut) + △f(u) = 0, (x, t) ∈ Ω× R+,u|αΩ=0,△u|αΩ=0,u(x,0) =u0(x), ut(x,0) = u1(x),where g(ut) = |ut|m-1ut,f(u) =|u|p-1u, p > 1, m≥1. By means of Faedo-Galerkin method and Fixed-point argument, we obtain the existence and uniqueness of local solu-tion. Global existence of solution is proved for p < m. The sufficient conditions of finite time blow-up of solutions are given for 1 < m <p. Moreover, we derive the global exis-tence, decay estimation and finite time blow-up of solutions by potential well method for E(0) < d.