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.identifier.wosut WOS:000469920100003 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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