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Journal of Applied Analysis

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

Managing Editor: Gajek, Leslaw

2 Issues per year

CiteScore 2016: 0.39

SCImago Journal Rank (SJR) 2016: 0.236
Source Normalized Impact per Paper (SNIP) 2016: 0.627

Mathematical Citation Quotient (MCQ) 2016: 0.14

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Volume 15, Issue 2 (Jan 2009)

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

K. T. Joseph
  • School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. e-mail:
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Published Online: 2010-06-09 | DOI: https://doi.org/10.1515/JAA.2009.247


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

About the article

Received: 2008-02-21

Revised: 2009-01-05

Published Online: 2010-06-09

Published in Print: 2009-12-01

Citation Information: Journal of Applied Analysis, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/JAA.2009.247.

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