On the well-posedness of entropy solutions for conservation lawswith source terms

Young-Sam Kwon

doi:10.3934/dcds.2009.25.933

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2009, Volume 25, Issue 3: 933-949. Doi: 10.3934/dcds.2009.25.933

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On the well-posedness of entropy solutions for conservation laws with source terms

Young-Sam Kwon^1,

1.
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Zitna' 25, 115 67 Praha 1

Received: September 30, 2008

Revised: February 28, 2009

Published: August 2009

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Abstract

In this paper we study the initial boundary value problems for scalar conservation laws with source terms possessing limited regularity. We first define a strong trace of large class of entropy solutions of scalar conservation laws with source terms at the boundary $(0,T)\times\{0\}$ reached by $L^1$ in order to find a good boundary condition and we prove the well-posedness for scalar conservation laws with source terms. The proof is based on the kinetic formulation and the compensated compactness method.

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Mathematics Subject Classification: Primary: 35L65; Secondary: 35B05, 35B65.

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