Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 35 No. 1 (2017): Revista Integración
Research and Innovation Articles

Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, week solutions and the entropy condition

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  • Edgardo Pérez,
  • Krzysztof Rózga
Edgardo Pérez
Université de Brest, Département de Mathématiques, Brest, France.
Krzysztof Rózga
University of Puerto Rico at Mayaguez, Department of Mathematical Sciences,
DOI: https://doi.org/10.18273/revint.v35n1-2017002

Published 2017-08-09

Keywords

  • Weak solution,
  • entropy condition,
  • conservation laws,
  • genuinely nonlinear,
  • p-system

How to Cite

Pérez, E., & Rózga, K. (2017). Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, week solutions and the entropy condition. Revista Integración, Temas De matemáticas, 35(1), 11–36. https://doi.org/10.18273/revint.v35n1-2017002

Abstract

We consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a functionW. We consider four forms of W. These are St.Venant-Kirchhoff, Ogden, Kirchhoff modified, Blatz-Ko-Ogden forms. In each of those cases we termine the conditions for the parameters μ, λ and f, under which the corresponding system is hyperbolic and genuinely nonlinear. We also establish what it means a weak solution of an initial and boundary value problem. Finally we ask if such solutions satisfy the entropy condition. For a standard entropy function we provide a complete answer, except of the Blatz-Ko-Ogden case. For a general strictly convex entropy function the result is that for the initial value of velocity function near zero these solutions satisfy the entropy condition, under the assumption of hyperbolicity and genuine nonlinearity.

MSC2010: 35L04, 35L60, 35L65, 35L67.

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