Global nonexistence of arbitrary initial energy solutions of viscoelastic equation with nonlocal boundary damping
The main goal of this paper is to investigate the blowing-up solutions to the initial value problem for the viscoelastic wave equation \[ u_{tt} - \Delta u + \int^t_0g(t - \tau)\text{div}(a(x)\nabla u(x,\tau))d\tau + u_t = 0\quad\text{in}\;\Omega \times (0,\infty) \] under boundary damping. The aim is to give a sufficient condition on the initial datum under which the solution blows up in finite time. The method of the proof is based on the concavity argument.
scientific article; zbMATH DE number 6137987