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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.