Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd

Published

Journal Article

© 2019 International Press. 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. Wellposedness 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.

Full Text

Duke Authors

Cited Authors

  • De Hoop, MV; Liu, JG; Markowich, PA; Ussembayev, NS

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 17 / 1

Start / End Page

  • 61 - 79

Electronic International Standard Serial Number (EISSN)

  • 1945-0796

International Standard Serial Number (ISSN)

  • 1539-6746

Digital Object Identifier (DOI)

  • 10.4310/cms.2019.v17.n1.a3

Citation Source

  • Scopus