Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Shock wave formation process for a multidimensional scalar conservation law

Authors: V. G. Danilov and D. Mitrovic
Journal: Quart. Appl. Math. 69 (2011), 613-634
MSC (2000): Primary 35L65, 35L67
DOI: https://doi.org/10.1090/S0033-569X-2011-01234-9
Published electronically: June 28, 2011
MathSciNet review: 2893992
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Abstract: We construct a global smooth approximate solution to a multidimensional scalar conservation law describing the shock wave formation process for initial data with small variation. In order to solve the problem, we modify the method of characteristics by introducing ``new characteristics'', nonintersecting curves along which the (approximate) solution to the problem under study is constant. The procedure is based on the weak asymptotic method, a technique which appeared to be rather powerful for investigating nonlinear waves interactions.

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Additional Information

V. G. Danilov
Affiliation: Moscow Technical University of Communication and Informatics, Aviamotornaya 8a, 111024 Moscow, Russia
Email: danilov@miem.edu.ru

D. Mitrovic
Affiliation: Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000 Podgorica, Montenegro
Address at time of publication: Faculty of Mathematics, University of Bergen, Johannes Bruns gate 12, 5007 Bergen
Email: matematika@t-com.me

DOI: https://doi.org/10.1090/S0033-569X-2011-01234-9
Keywords: global approximate solution, weak asymptotic method
Received by editor(s): April 24, 2009
Published electronically: June 28, 2011
Additional Notes: The work of V. G. Danilov is supported by RFFI grant 05-01-00912, DFG Project 436 RUS 113/895/0-1.
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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