Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities

@inproceedings{Guo2016BlowupOA,
  title={Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities},
  author={Yanqiu Guo and Mohammad Rammaha and Sawanya Sakuntasathien},
  year={2016}
}
We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source: { utt − k(0) u − ∫∞ 0 k ′(s) u(t − s)ds + |ut |m−1ut = |u|p−1u, in × (0, T ), u(x, t) = u0(x, t), in × (−∞,0], where is a bounded domain in R3 with a Dirichlét boundary condition. The relaxation kernel k is monotone decreasing and k(∞) = 1. We… CONTINUE READING