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A General Study of a Commutation Relation Given by L. Tartar

  • Denis Serre
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 2)

Abstract

Let (S) be a strictly hyperbolic system of two conservation laws with two unknown functions:
$$ \left\{ {\begin{array}{*{20}c} {u_t + f(u,v)_x = 0} \\ {v_t + g(u,v)_x = 0} \\ \end{array} } \right.\begin{array}{*{20}c} {x \in R,} & {t > 0} \\ \end{array} $$
(S)
L. Tartar [1] studued the parabolic approximation of this system, intending to prove the existence of a weak entropy to the Caucy problem:
$$(S_\varepsilon ,\varepsilon > 0)\left\{ {\begin{array}{*{20}c} {u_t^\varepsilon + f(u^\varepsilon ,v^\varepsilon )_x = \varepsilon u_{XX}^\varepsilon ,} \\ {v_t^\varepsilon + g(u^\varepsilon ,v^\varepsilon )_x = \varepsilon v_{XX}^\varepsilon .} \\ \end{array} } \right. $$

Keywords

Hyperbolic System Nonlinear Elasticity Entropy Solution Characteristic Field Dirac Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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    L. Tartar: Compensated Compactness and applications to POE, in Research Notes in Maths, Nonlinear Analysis and Mechanics. Heriot-Watt Symposium, 4. 1979. Knops Ed. Pitman Press.Google Scholar
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Denis Serre
    • 1
  1. 1.U.E.R de SciencesSt.-Etienne, CedexFrance

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