Measure-valued solutions and well-posedness of multi-dimensional conservation laws in a bounded domain (Q5946167)

The authors study an initial-boundary value problem for a scalar conservation law. Existence, uniqueness, and compactness results are established in a class of entropy measure-valued solutions, following DiPerna and Szepessy. The new features here lie in the treatment of the boundary condition, which the authors are able to formulate by relying only on \(L^p\) uniform bound. The obtained results are also applied to prove the strong convergence of diffusive approximations.