Convergence of approximate solutions to scalar conservation laws by degenerate diffusion

Pierangelo Marcati

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In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in $L^{\infty}$ . Lastly, we study the behaviour of this solution and its stability properties...