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Plane-wave analysis of a hyperbolic system of equations with relaxation in R^d

dc.contributor.authorde Hoop, Maarten V.
dc.contributor.authorLiu, Jian-Guo
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorUssembayev, Nail S.
dc.date.accessioned2019-07-10T07:30:53Z
dc.date.available2019-07-10T07:30:53Z
dc.date.issued2019
dc.identifier.citationDe 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.doi10.4310/cms.2019.v17.n1.a3
dc.identifier.urihttp://hdl.handle.net/10754/655965
dc.description.abstractWe 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.sponsorshipM.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.isoen
dc.publisherInternational Press of Boston
dc.rightsArchived with thanks to Communications in Mathematical Sciences
dc.subjectcharacteristic fields of constant multiplicity
dc.subjecteigenvalues
dc.subjectviscoelasticity
dc.subjectmemory effect
dc.subjectZener model
dc.subjectstability
dc.subjectenergy methods
dc.titlePlane-wave analysis of a hyperbolic system of equations with relaxation in R^d
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalCommunications in Mathematical Sciences
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Computational and Applied Mathematics, Rice University, Houston, Texas, U.S.A.
dc.contributor.institutionDepartments of Mathematics and Physics, Duke University, Durham, North Carolina, U.S.A.
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
pubs.publication-statusPublished
kaust.personMarkowich, Peter A.
kaust.personUssembayev, Nail S.
refterms.dateFOA2019-07-10T07:30:55Z


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