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Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

2 Issues per year


SCImago Journal Rank (SJR): 0.752
Source Normalized Impact per Paper (SNIP): 1.104

Mathematical Citation Quotient 2013: 0.13

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A System of Two Conservation Laws with Flux Conditions and Small Viscosity

K. T. Joseph1

1School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. e-mail:

Citation Information: Journal of Applied Analysis. Volume 15, Issue 2, Pages 247–267, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: 10.1515/JAA.2009.247, June 2010

Publication History

Received:
2008-02-21
Revised:
2009-01-05
Published Online:
2010-06-09

Abstract

We construct explicit solutions of a system of two conservation laws with small viscosity in the quarter plane {(x, t) : x > 0, t > 0}, with initial conditions at t = 0 and flux conditions at x = 0. We derive a formula for the limit as viscosity goes to zero which generally belongs to the space of locally bounded Borel measures. This limit satisfies the inviscid equation, in the sense of LeFloch [An existence and uniqueness result for two non-strictly hyperbolic systems, Springer, 1990]. We also treat more general initial and boundary datas and obtain solution in the algebra of generalized functions of Colombeau [C. R. Acad. Sci. Paris Ser. I Math. 317: 851–855, 1993, C. R. Acad. Sci. Paris Ser. I Math. 319: 1179–1183, 1994].

Key words and phrases.: δ-waves; exact solutions with flux condition

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[1]
K. T. Joseph and G. D. Veerappa Gowda
Advances in Pure and Applied Mathematics, 2011, Volume 2, Number 2

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