Plane-wave analysis of a hyperbolic system of equations with relaxation in $\mathbb{R}^{d}$
Analysis of PDEs
2018-09-28 v1
Abstract
We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation system is an example of a non-strictly hyperbolic system satisfying Majda's block structure condition. Well-posedness of the associated Cauchy problem is established by showing that the symbol of the spatial derivatives is uniformly diagonalizable with real eigenvalues. A long-time stability result is obtained by plane-wave analysis when the memory term allows for dissipation of energy.
Keywords
Cite
@article{arxiv.1809.10649,
title = {Plane-wave analysis of a hyperbolic system of equations with relaxation in $\mathbb{R}^{d}$},
author = {Maarten V. de Hoop and Jian-Guo Liu and Peter A. Markowich and Nail S. Ussembayev},
journal= {arXiv preprint arXiv:1809.10649},
year = {2018}
}
Comments
19 pages