Minimal entropy conditions for Burgers equation

Camillo De Lellis, Felix Otto, and Michael Westdickenberg
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Submission date: 10. Jul. 2003
Pages: 16
published in: Quarterly of applied mathematics, 62 (2004) 4, p. 687-700 
MSC-Numbers: 35L65, 35L67
Keywords and phrases: entropy solutions, entropy conditions, viscosity solutions
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Abstract:
We consider strictly convex, 1-d scalar conservation laws. We show that a single strictly convex entropy is sufficient to characterize a Kruzhkov solution. The proof uses the concept of viscosity solution for the related Hamilton-Jacobi equation.