Abstract
This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms
Highlights
The interaction between the weak damping term and the source term are considered by many authors
Under some appropriate assumptions on g, by introducing potential wells they obtained the existence of global solution and the explicit exponential energy decay estimates
We prove that Problem (4)-(6) has a global weak solution assuming small initial data
Summary
T his paper deals with the initial boundary value problem of the dispersive wave equation with memory and source terms t utt − ∆u + α∆2u − g(t − τ)∆2u(τ)dτ + ut = |u|p−1u, x ∈ Ω, t > 0,. Our main goal in the present paper is to discuss the global solutions and general decay to the following weakly damped wave equation with dispersive term, the fourth order memory term and the nonlinear source term t utt − ∆u + ∆2u − g(t − τ)∆2u(τ)dτ + ut = |u|p−1u in Ω × R+,.
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