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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

Online
ISSN
1869-6082
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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

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

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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[1]
Engu Satynarayana, Manas R. Sahoo, and Manasa M
Communications on Pure and Applied Analysis, 2016, Volume 16, Number 1, Page 253
[2]
K. T. Joseph and G. D. Veerappa Gowda
Advances in Pure and Applied Mathematics, 2011, Volume 2, Number 2

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