Shock dynamics in layered periodic media
dc.contributor.author | Ketcheson, David I. | |
dc.contributor.author | Leveque, Randall J. | |
dc.date.accessioned | 2014-11-03T16:17:16Z | |
dc.date.available | 2014-11-03T16:17:16Z | |
dc.date.issued | 2012 | |
dc.identifier.citation | Shock dynamics in layered periodic media 2012, 10 (3):859 Communications in Mathematical Sciences | |
dc.identifier.issn | 15396746 | |
dc.identifier.issn | 19450796 | |
dc.identifier.doi | 10.4310/CMS.2012.v10.n3.a7 | |
dc.identifier.uri | http://hdl.handle.net/10754/333598 | |
dc.description.abstract | Solutions 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.iso | en | |
dc.publisher | International Press of Boston | |
dc.relation.url | http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0010/0003/a007/ | |
dc.relation.url | http://arxiv.org/abs/1105.2892 | |
dc.rights | Archived with thanks to Communications in Mathematical Sciences | |
dc.subject | shock waves | |
dc.subject | periodic media | |
dc.subject | dispersive shocks | |
dc.subject | solitary waves | |
dc.title | Shock dynamics in layered periodic media | |
dc.type | Article | |
dc.contributor.department | Applied Mathematics and Computational Science Program | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.contributor.department | Numerical Mathematics Group | |
dc.identifier.journal | Communications in Mathematical Sciences | |
dc.eprint.version | Publisher's Version/PDF | |
dc.contributor.institution | Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195-2420, USA | |
dc.contributor.affiliation | King Abdullah University of Science and Technology (KAUST) | |
dc.identifier.arxivid | 1105.2892 | |
kaust.person | Ketcheson, David I. | |
dc.version | v1 | |
refterms.dateFOA | 2018-06-13T15:33:22Z | |
dc.date.posted | 2011-05-14 |
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Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
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