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September  2009, 25(3): 933-949. doi: 10.3934/dcds.2009.25.933

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, Czech Republic

Received  October 2008 Revised  March 2009 Published  August 2009

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.
Keywords: averaging lemma., Conservation laws with source terms, boundary value problems, kinetic formulation, trace theorem.
Mathematics Subject Classification: Primary: 35L65; Secondary: 35B05, 35B6.
Citation: Young-Sam Kwon. On the well-posedness of entropy solutions for conservation laws with source terms. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 933-949. doi: 10.3934/dcds.2009.25.933
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