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
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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35L65, 35L67

Retrieve articles in all journals with MSC (2000): 35L65, 35L67

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.

Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website