Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping
Analysis of PDEs
2014-10-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1308.0720,
title = {Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping},
author = {Yanqiu Guo and Mohammad A. Rammaha and Sawanya Sakuntasathien and Edriss S. Titi and Daniel Toundykov},
journal= {arXiv preprint arXiv:1308.0720},
year = {2014}
}
Comments
The 2nd version includes a new proof of the energy identity