Shock dynamics in layered periodic media

David I. Ketcheson, Randall J. Leveque

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)859-874
Number of pages16
JournalCommunications in Mathematical Sciences
Volume10
Issue number3
DOIs
StatePublished - 2012

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Fingerprint Dive into the research topics of 'Shock dynamics in layered periodic media'. Together they form a unique fingerprint.

Cite this