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 **-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 -shocks. The *weak asymptotics method* developed by the authors is used to describe the propagation of -shock waves to the three types of systems of conservation laws and derive the corresponding Rankine-Hugoniot conditions for -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)

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Brown University