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A uniqueness criterion for viscous limits of boundary Riemann problems


Christoforou, C; Spinolo, L V (2011). A uniqueness criterion for viscous limits of boundary Riemann problems. Journal of Hyperbolic Differential Equations, 8(3):507-544.

Abstract

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In this paper, we establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that, under reasonable assumptions, the self-similar second-order approximation and the classical viscous approximation provide the same limit. Our analysis applies to both the characteristic and the non characteristic case. We require neither genuine nonlinearity nor linear degeneracy of the characteristic fields.

Abstract

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In this paper, we establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that, under reasonable assumptions, the self-similar second-order approximation and the classical viscous approximation provide the same limit. Our analysis applies to both the characteristic and the non characteristic case. We require neither genuine nonlinearity nor linear degeneracy of the characteristic fields.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:17 Feb 2012 20:31
Last Modified:05 Apr 2016 15:33
Publisher:World Scientific Publishing Co.
ISSN:0219-8916 (P) 1793-6993 (E)
Publisher DOI:https://doi.org/10.1142/S0219891611002482
Related URLs:http://arxiv.org/abs/1007.3931

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