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dc.contributor.authorKetcheson, David I.
dc.contributor.authorLeveque, Randall J.
dc.date.accessioned2014-11-03T16:17:16Z
dc.date.available2014-11-03T16:17:16Z
dc.date.issued2012
dc.identifier.citationShock dynamics in layered periodic media 2012, 10 (3):859 Communications in Mathematical Sciences
dc.identifier.issn15396746
dc.identifier.issn19450796
dc.identifier.doi10.4310/CMS.2012.v10.n3.a7
dc.identifier.urihttp://hdl.handle.net/10754/333598
dc.description.abstractSolutions of constant-coeffcient nonlinear hyperbolic PDEs generically develop shocks, even if the initial data is smooth. Solutions of hyperbolic PDEs with variable coeffcients can behave very differently. We investigate formation and stability of shock waves in a one-dimensional periodic layered medium by a computational study of time-reversibility and entropy evolution. We find that periodic layered media tend to inhibit shock formation. For small initial conditions and large impedance variation, no shock formation is detected even after times much greater than the time of shock formation in a homogeneous medium. Furthermore, weak shocks are observed to be dynamically unstable in the sense that they do not lead to significant long-term entropy decay. We propose a characteristic condition for admissibility of shocks in heterogeneous media that generalizes the classical Lax entropy condition and accurately predicts the formation or absence of shocks in these media.
dc.language.isoen
dc.publisherInternational Press of Boston
dc.relation.urlhttp://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0010/0003/a007/
dc.relation.urlhttp://arxiv.org/abs/1105.2892
dc.rightsArchived with thanks to Communications in Mathematical Sciences
dc.subjectshock waves
dc.subjectperiodic media
dc.subjectdispersive shocks
dc.subjectsolitary waves
dc.titleShock dynamics in layered periodic media
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Mathematics Group
dc.identifier.journalCommunications in Mathematical Sciences
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195-2420, USA
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxividarXiv:1105.2892
kaust.personKetcheson, David I.
dc.versionv1
refterms.dateFOA2018-06-13T15:33:22Z
dc.date.posted2011-05-14


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