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An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. (English) Zbl 1053.35015

Authors’ abstract: We study the parabolic approximation of a multidimensional scalar conservation law with initial and boundary conditions. We prove that the rate of convergence of the viscous approximation to the weak entropy solution is of order \(\eta^{1/3}\), where \(\eta\) is the size of the artificial viscosity. We use a kinetic formulation and kinetic techniques for initial-boundary value problems developed by the last two authors in a previous work.

MSC:

35A35 Theoretical approximation in context of PDEs
35L65 Hyperbolic conservation laws
35F25 Initial value problems for nonlinear first-order PDEs
35F30 Boundary value problems for nonlinear first-order PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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References:

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