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Solution of a transport equation with discontinuous coefficients

  • Abhishek Das EMAIL logo and K. T. Joseph

Abstract

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.

MSC 2010: 35F61; 35L50; 35R05

Funding statement: This work was done while the second author was a Raja Ramanna Fellow at TIFR CAM, Bangalore, India.

Acknowledgements

The authors are thankful to the anonymous referee for valuable comments and suggestions on an early version, which helped them to improve the paper in the present form.

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Received: 2019-10-11
Revised: 2020-08-10
Accepted: 2020-08-15
Published Online: 2021-02-02
Published in Print: 2021-12-01

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