Obstacle problems for scalar conservation laws (Q2781489)

The author considers bilateral obstacle problem for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. First a suitable entropy formulation ensuring uniqueness is given. Next, using the penalization method, an existence of a solution is shown. Finally the behaviour of the solution and its stability properties with respect to the associated obstacle function is considered. In the proofs the author exploits some results of [\textit{S. N. Kruzhkov}, Math USSR, Sb. 10, 217-243 (1970); translation from Mat. Sb., n. Ser. 81(123), 228-255 (1970; Zbl 0202.11203), \textit{C. Bardos, A.-Y. Le Roux} and \textit{N. C. Nédélec}, Commun. Partial Differ. Equations 4, 1017-1034 (1979; Zbl 0418.35024), \textit{J. M. Ball}, Lect. Notes Phys. 344, 207-215 (1989) and \textit{J. Nečas, J. Malek, M. Rokyta} and \textit{M. Ruzicka}, Weak and measure-valued solutions to evolutionary PDEs. Chapman \& Hall, London (1996; Zbl 0851.35002)].