Abstract
In this paper, we consider the initial boundary value problem of the double dispersive-dissipative wave equation with nonlinear damping and source terms. By the combination of the Galerkin method and the monotonicity-compactness method, the existence of global solutions is obtained with the least amount of a priori estimates. Moreover, the asymptotic behavior of global solutions is investigated under some assumptions on the initial data.
Highlights
1 Introduction This paper deals with the initial boundary value problem of the double dispersivedissipative wave equation with nonlinear damping and source terms utt – u – β ut + γ u – δ utt + g(ut) = f (u), x ∈, t >, ( . )
In the absence of a dissipative term, double dispersive terms (β = γ = δ = ), and a damping term g(ut) =, the model reduces to the common semilinear wave equation utt – u = f (u), x ∈, t >
We investigate the initial boundary value problem for the double dispersive wave equation with a strong dissipation term, a nonlinear damping and source terms:
Summary
In , Shang [ ] studied the initial boundary value problem of the fourth-order nonlinear wave equation ) reduces to the fourthorder dispersive-dissipative wave equation utt – u + ut – utt + ut = |u|p– u, x ∈ , t > , In , Xu and Yang [ ] investigated the initial boundary value problem of As far as we know, there have been no results up till on the initial boundary value problem for a nonlinear wave equation with double dispersive terms u, utt, the strong dissipation term ut, the nonlinear damping term g(ut), and the nonlinear source term f (u). We investigate the initial boundary value problem for the double dispersive wave equation with a strong dissipation term, a nonlinear damping and source terms:.
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