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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.