Abstract
In this paper, we consider the long time behavior of solutions of the initial value problem for the viscoelastic wave equation under boundary damping \begin{eqnarray*} u_{tt}-\Delta u+\int_0^t g(t-\tau)\text{div}(a(x)\nabla u(\tau))d\tau+u_t=0 &\text{in}\,\Omega\times(0,\infty). \end{eqnarray*} For the low initial energy case, which is the non-positive initial energy, based on concavity argument we prove the blow up result. As for the high initial energy case, we give out sufficient conditions of the initial datum such that the solution blows up in finite time.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.