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Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
Date
2012Preprint Posting Date
2011-05-14Permanent link to this record
http://hdl.handle.net/10754/333598
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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.Citation
Shock dynamics in layered periodic media 2012, 10 (3):859 Communications in Mathematical SciencesPublisher
International Press of BostonarXiv
1105.2892Additional Links
http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0010/0003/a007/http://arxiv.org/abs/1105.2892
ae974a485f413a2113503eed53cd6c53
10.4310/CMS.2012.v10.n3.a7