LAX SHOCKS IN MIXED-TYPE SYSTEMS OF CONSERVATION LAWS-Reference-Cited by-同舟云学术

LAX SHOCKS IN MIXED-TYPE SYSTEMS OF CONSERVATION LAWS

Published:2008-06 Issue:02 Volume:05 Page:295-315
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

MAILYBAEV ALEXEI A.¹,MARCHESIN DAN²

Affiliation:

1. Institute of Mechanics, Moscow State Lomonosov University, Michurinsky pr. 1, 119192 Moscow, Russia

2. Instituto Nacional de Matemática Pura e Aplicada — IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro RJ, Brazil

Abstract

Small amplitude shocks involving a state with complex characteristic speeds arise in mixed-type systems of two or more conservation laws. We study such shocks in detail in the generic case, when they appear near the codimension-1 elliptic boundary. Then we classify all exceptional codimension-2 states on smooth parts of the elliptic boundary. Asymptotic formulae describing shock curves near regular and exceptional states are derived. The type of singularity at the exceptional point depends on the second and third derivatives of the flux function. The main application is understanding the structure of small amplitude Riemann solutions where one of the initial states lies in the elliptic region.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891608001490

Reference23 articles.

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4. Nonexistence of Riemann solutions for a quadratic model deriving from petroleum engineering

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