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Article Contents

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

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

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