Plane-wave analysis of a hyperbolic system of equations with relaxation in R^d
dc.contributor.author | de Hoop, Maarten V. | |
dc.contributor.author | Liu, Jian-Guo | |
dc.contributor.author | Markowich, Peter A. | |
dc.contributor.author | Ussembayev, Nail S. | |
dc.date.accessioned | 2019-07-10T07:30:53Z | |
dc.date.available | 2019-07-10T07:30:53Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | 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 $\mathbb{R}^d$. Communications in Mathematical Sciences, 17(1), 61–79. doi:10.4310/cms.2019.v17.n1.a3 | |
dc.identifier.doi | 10.4310/cms.2019.v17.n1.a3 | |
dc.identifier.uri | http://hdl.handle.net/10754/655965 | |
dc.description.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. 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. | |
dc.description.sponsorship | M.V.d.H. gratefully acknowledges support from the Simons Foundation under the MATH + X program, the National Science Foundation under grant DMS-1559587, and the corporate members of the GeoMathematical Group at Rice University. J.-G.L. is supported by the National Science Foundation under grant DMS-1812573 and KI-Net RNMS11-07444. | |
dc.language.iso | en | |
dc.publisher | International Press of Boston | |
dc.rights | Archived with thanks to Communications in Mathematical Sciences | |
dc.subject | characteristic fields of constant multiplicity | |
dc.subject | eigenvalues | |
dc.subject | viscoelasticity | |
dc.subject | memory effect | |
dc.subject | Zener model | |
dc.subject | stability | |
dc.subject | energy methods | |
dc.title | Plane-wave analysis of a hyperbolic system of equations with relaxation in R^d | |
dc.type | Article | |
dc.contributor.department | Applied Mathematics and Computational Science | |
dc.contributor.department | Applied Mathematics and Computational Science Program | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.identifier.journal | Communications in Mathematical Sciences | |
dc.eprint.version | Publisher's Version/PDF | |
dc.contributor.institution | Department of Computational and Applied Mathematics, Rice University, Houston, Texas, U.S.A. | |
dc.contributor.institution | Departments of Mathematics and Physics, Duke University, Durham, North Carolina, U.S.A. | |
dc.contributor.affiliation | King Abdullah University of Science and Technology (KAUST) | |
pubs.publication-status | Published | |
kaust.person | Markowich, Peter A. | |
kaust.person | Ussembayev, Nail S. | |
refterms.dateFOA | 2019-07-10T07:30:55Z |
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