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dc.contributor.authorKetcheson, David I.
dc.contributor.authorQuezada de Luna, Manuel
dc.date.accessioned2020-09-06T11:56:32Z
dc.date.available2019-11-13T00:20:26Z
dc.date.available2020-09-06T11:56:32Z
dc.date.issued2020-07-28
dc.date.submitted2019-09-11
dc.identifier.citationKetcheson, D. I., & Quezada de Luna, M. (2020). Effective Rankine–Hugoniot conditions for shock waves in periodic media. Communications in Mathematical Sciences, 18(4), 1023–1040. doi:10.4310/cms.2020.v18.n4.a6
dc.identifier.issn1945-0796
dc.identifier.issn1539-6746
dc.identifier.doi10.4310/CMS.2020.V18.N4.A6
dc.identifier.urihttp://hdl.handle.net/10754/659990
dc.description.abstractSolutions of first-order nonlinear hyperbolic conservation laws typically develop shocks infinite time even from smooth initial conditions. However, in heterogeneous media with rapid spatial variation, shock formation may be delayed or avoided. When shocks do form in such media, their speed of propagation depends on the material structure. We investigate conditions for shock formation and propagation in heterogeneous media. We focus on the propagation of plane waves in two-dimensional media with a periodic structure that changes in only one direction. We propose an estimate for the speed of the shocks that is based on the Rankine-Hugoniot conditions applied to a leading-order homogenized (constant coefficient) system. We verify this estimate via numerical simulations using different nonlinear constitutive relations and layered and smoothly varying media with a periodic structure. In addition, we discuss conditions and regimes under which shocks form in this type of media.
dc.description.sponsorshipThis work was supported by funding from King Abdullah University of Science & Technology (KAUST).
dc.publisherInternational Press of Boston
dc.relation.urlhttps://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0018/0004/a006/
dc.rightsArchived with thanks to Communications in Mathematical Sciences
dc.titleEffective rankine-hugoniot conditions for shock waves in 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.rights.embargodate2021-01-13
dc.eprint.versionPost-print
dc.identifier.volume18
dc.identifier.issue4
dc.identifier.pages1023-1040
dc.identifier.arxivid1909.04937
kaust.personKetcheson, David I.
kaust.personQuezada de Luna, Manuel
dc.date.accepted2020-01-13
dc.identifier.eid2-s2.0-85089511972
refterms.dateFOA2019-11-13T00:21:39Z
dc.date.published-online2020-07-28
dc.date.published-print2020
dc.date.posted2019-09-11


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