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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 . Lastly, we study the behaviour of this solution and its stability properties with...
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
. Lastly, we study the behaviour of this solution and its stability...
We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of , . In order to prove the -convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in together with a weak formulation of boundary conditions for scalar conservation laws.
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