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

Published electronically:
June 28, 2011

MathSciNet review:
2893992

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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:
http://dx.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.