Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Wave interactions and stability of the Riemann solution for a strictly hyperbolic system of conservation laws


Authors: Anupam Sen, T. Raja Sekhar and V. D. Sharma
Journal: Quart. Appl. Math. 75 (2017), 539-554
MSC (2010): Primary 35L45, 35L65, 58J45; Secondary 35Q35, 35L67
DOI: https://doi.org/10.1090/qam/1466
Published electronically: March 15, 2017
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Abstract: In this article, we study the interaction of delta shock waves for the one-dimensional strictly hyperbolic system of conservation laws with split delta function. We prove that Riemann solutions are stable under local small perturbations of the Riemann initial data. The global structure and large time asymptotic behaviour of the perturbed Riemann solutions are constructed and analyzed case by case.


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Additional Information

Anupam Sen
Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-2, India
Email: sen.anupam123@gmail.com

T. Raja Sekhar
Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-2, India
Email: trajasekhar@maths.iitkgp.ernet.in

V. D. Sharma
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Mumbai-76, India
Email: vsharma@math.iitb.ac.in

DOI: https://doi.org/10.1090/qam/1466
Keywords: Delta shock wave, delta contact discontinuity, wave interactions, Riemann problem, split delta function
Received by editor(s): October 6, 2016
Received by editor(s) in revised form: February 5, 2017
Published electronically: March 15, 2017
Article copyright: © Copyright 2017 Brown University


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