Abstract
The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u \) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.
Highlights
L et Ω be a bounded domain in RN (N ≥ 1) with smooth boundary ∂Ω
The motivation of our work is due to the initial boundary problem of the double dispersive-dissipative wave equation with nonlinear damping and source terms utt − ∆u − ∆utt + ∆2u − ∆ut + a|ut|m−2ut = b|u|p−2u, x ∈ Ω, t > 0
The global solutions are constructed by means of the Galerkin approximations and the general decay is obtained by employing the technique used in [7]
Summary
We consider the initial-boundary value problem: utt − ∆u − ∆utt + ∆2u − g ∗ ∆2u − ∆ut. The motivation of our work is due to the initial boundary problem of the double dispersive-dissipative wave equation with nonlinear damping and source terms utt − ∆u − ∆utt + ∆2u − ∆ut + a|ut|m−2ut = b|u|p−2u, x ∈ Ω, t > 0,. = |u|p−1u, u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, t > 0, x ∈ ∂Ω, t > 0, x ∈ Ω, in a bounded domain and p > 1 He investigated the small data global weak solutions and general decay of solutions, respectively. It is interesting to prove that problem (1) has a global weak solution assuming small initial data. The global solutions are constructed by means of the Galerkin approximations and the general decay is obtained by employing the technique used in [7]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
