Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping
- Author(s): Guo, Y
- Rammaha, MA
- Sakuntasathien, S
- Titi, ES
- Toundykov, D
- et al.
Published Web Locationhttps://doi.org/10.1016/j.jde.2014.07.009
© 2014 Elsevier Inc. Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.