The Boundary Riemann Solver Coming from the Real Vanishing Viscosity Approximation |
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Authors: | Stefano Bianchini Laura V Spinolo |
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Institution: | (1) SISSA-ISAS, via Beirut 2-4, 34014 Trieste, Italy;(2) Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2370, USA |
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Abstract: | We study the limit of the hyperbolic–parabolic approximation
The function is defined in such a way as to guarantee that the initial boundary value problem is well posed even if is not invertible. The data and are constant. When is invertible, the previous problem takes the simpler formAgain, the data and are constant. The conservative case is included in the previous formulations. Convergence of the , smallness of the total variation and other technical hypotheses are assumed, and a complete characterization of the limit
is provided. The most interesting points are the following: First, the boundary characteristic case is considered, that is,
one eigenvalue of can be 0. Second, as pointed out before, we take into account the possibility that is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta
relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if
this condition is not satisfied, then pathological behaviors may occur. |
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Keywords: | |
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