Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd
Publication
, Journal Article
De Hoop, MV; Liu, JG; Markowich, PA; Ussembayev, NS
Published in: Communications in Mathematical Sciences
January 1, 2019
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.
Duke Scholars
Published In
Communications in Mathematical Sciences
DOI
EISSN
1945-0796
ISSN
1539-6746
Publication Date
January 1, 2019
Volume
17
Issue
1
Start / End Page
61 / 79
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
De Hoop, M. V., Liu, J. G., Markowich, P. A., & Ussembayev, N. S. (2019). Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd. Communications in Mathematical Sciences, 17(1), 61–79. https://doi.org/10.4310/cms.2019.v17.n1.a3
De Hoop, M. V., J. G. Liu, P. A. Markowich, and N. S. Ussembayev. “Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd.” Communications in Mathematical Sciences 17, no. 1 (January 1, 2019): 61–79. https://doi.org/10.4310/cms.2019.v17.n1.a3.
De Hoop MV, Liu JG, Markowich PA, Ussembayev NS. Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd. Communications in Mathematical Sciences. 2019 Jan 1;17(1):61–79.
De Hoop, M. V., et al. “Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd.” Communications in Mathematical Sciences, vol. 17, no. 1, Jan. 2019, pp. 61–79. Scopus, doi:10.4310/cms.2019.v17.n1.a3.
De Hoop MV, Liu JG, Markowich PA, Ussembayev NS. Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd. Communications in Mathematical Sciences. 2019 Jan 1;17(1):61–79.
Published In
Communications in Mathematical Sciences
DOI
EISSN
1945-0796
ISSN
1539-6746
Publication Date
January 1, 2019
Volume
17
Issue
1
Start / End Page
61 / 79
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics