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Solution of a transport equation with discontinuous coefficients

Das Abhishek, Joseph K. T.

Journal of Applied Analysis

2021

Vol. 27, nr 2

219--238

In this article, we study initial and initial-boundary value problems for a non-strictly hyperbolic system whose characteristic speed is not smooth and takes values in {−1, 0, 1}. We construct an explicit formula for the weak solution.We also study the interaction of waves and the large time asymptotic behavior of a solution for the case when the initial data is periodic with zero mean over the period and also for the case when the initial data has compact support.

A system of two conservation laws with flux conditions and small viscosity

Joseph K. T.

Journal of Applied Analysis

2014

Vol. 20, nr 1

This is an erratum to [J. Appl. Anal. 15 (2009), no. 2, 247–267], http://dx.doi.org/10.1515/JAA.2009.247. In this note the author would like to make a correction in formulas (2.12) and (2.13) for the limit limϵ→0(uϵ(x,t),vϵ(x,t)) stated in Theorem (2.1); there is no change in the proof.

A system of two conservation laws with flux conditions and small viscosity

Joseph K. T.

Journal of Applied Analysis

2009

Vol. 15, nr 2

247-267

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 [26]. We also treat more general initial and boundary datas and obtain solution in the algebra of generalized functions of Colombeau [9, 10].