Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Delta-shock wave type solution of hyperbolic systems of conservation laws

Authors: V. G. Danilov and V. M. Shelkovich
Journal: Quart. Appl. Math. 63 (2005), 401-427
MSC (2000): Primary 35L65; Secondary 35L67, 76L05
DOI: https://doi.org/10.1090/S0033-569X-05-00961-8
Published electronically: August 17, 2005
MathSciNet review: 2169026
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Abstract | References | Similar Articles | Additional Information

Abstract: For two classes of hyperbolic systems of conservation laws new definitions of a $\delta$-shock wave type solution are introduced. These two definitions give natural generalizations of the classical definition of the weak solutions. It is relevant to the notion of $\delta$-shocks. The weak asymptotics method developed by the authors is used to describe the propagation of $\delta$-shock waves to the three types of systems of conservation laws and derive the corresponding Rankine-Hugoniot conditions for $\delta$-shocks.

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Additional Information

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

V. M. Shelkovich
Affiliation: Department of Mathematics, St.-Petersburg State Architecture and Civil Engineering University, 2 Krasnoarmeiskaya 4, 190005, St. Petersburg, Russia
Email: shelkv@vs1567.spb.edu

DOI: https://doi.org/10.1090/S0033-569X-05-00961-8
Keywords: Hyperbolic systems of conservation laws, zero-pressure gas dynamics system, delta-shock wave type solutions, the Rankine--Hugoniot conditions of delta-shocks, the weak asymptotics method
Received by editor(s): August 5, 2003
Published electronically: August 17, 2005
Additional Notes: The first author (V. D.) was supported in part by Grant 05-01-00912 of Russian Foundation for Basic Research, SEP-CONACYT Grant 41421, SEP-CONACYT Grant 43208 (Mexico)
The second author (V. S.) was supported in part by DFG Project 436 RUS 113/593/3, Grant 02-01-00483 of Russian Foundation for Basic Research, and SEP-CONACYT Grant 41421, SEP-CONACYT Grant 43208 (Mexico)
Article copyright: © Copyright 2005 Brown University

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