A variational approach to the Riemann problem for hyperbolic conservation laws

Constantine M. Dafermos

doi:10.3934/dcds.2009.23.185

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2009, Volume 23, Issue 1&2: 185-195. Doi: 10.3934/dcds.2009.23.185

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A variational approach to the Riemann problem for hyperbolic conservation laws

Constantine M. Dafermos^1,

1.
Division of Applied Mathematics, Brown University, Providence, RI 02912

Received: November 30, 2007

Revised: March 31, 2008

Published: April 2009

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Abstract

Within the framework of strictly hyperbolic systems of conservation laws endowed with a convex entropy, it is shown that the admissible solution to the Riemann problem is obtained by minimizing the entropy production over all wave fans with fixed end-states.

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Mathematics Subject Classification: Primary: 35L65.

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