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We consider a scalar conservation law with relaxation in a bounded domain$\Omega$, which describes the macroscopic evolution of some interactingparticle system. The strength of the relaxation grows to infinity at$\partial\Omega$. We define the entropy solution $u \in L^\infty$ and provethat it is unique. When the relaxation is integrable, $u$ satisfies theboundary condition in [13], which allows the solution to attain values at$\partial\Omega$ different from the given data. When the relaxation is notintegrable, $u$ satisfies an energy estimate and turns out to be continuous at$\partial\Omega$ in a very weak sense.

Scalar conservation law in a bounded domain with strong relaxation at boundary