Asymptotic equations for conservation laws of mixed type

Moysey Brio; John K. Hunter

doi:10.1016/0165-2125(92)90046-5

Asymptotic equations for conservation laws of mixed type

Moysey Brio, John K. Hunter

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We derive canonical asymptotic equations for weakly nonlinear solutions of conservation laws of mixed type. When two real wave speeds coalesce and become complex, we obtain the transonic small disturbance equation which changes type from hyperbolic to elliptic. When the coefficient of the nonlinear term in the transonic small disturbance equation vanishes, we derive cubically nonlinear 2 × 2 asymptotic equations. These include canonical equations which are parabolic on a line in state space and strictly hyperbolic away from this line.

Original language	English (US)
Pages (from-to)	57-64
Number of pages	8
Journal	Wave Motion
Volume	16
Issue number	1
DOIs	https://doi.org/10.1016/0165-2125(92)90046-5
State	Published - Jul 1992

ASJC Scopus subject areas

Modeling and Simulation
General Physics and Astronomy
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/0165-2125(92)90046-5

Cite this

@article{6e7579733a5b4c72b409f0ed90072dea,

title = "Asymptotic equations for conservation laws of mixed type",

abstract = "We derive canonical asymptotic equations for weakly nonlinear solutions of conservation laws of mixed type. When two real wave speeds coalesce and become complex, we obtain the transonic small disturbance equation which changes type from hyperbolic to elliptic. When the coefficient of the nonlinear term in the transonic small disturbance equation vanishes, we derive cubically nonlinear 2 × 2 asymptotic equations. These include canonical equations which are parabolic on a line in state space and strictly hyperbolic away from this line.",

author = "Moysey Brio and Hunter, {John K.}",

note = "Funding Information: The work of M. Brio was partiallys upported by the NSF under grant DMS-8902097a nd by the Arizona Center for MathematicaSl ciences AFOSR ContractF 49620-86-C013T0h. e work of J.K. Hunter was partiallys upportedb y the NSF underg rantD MS-9011548.",

year = "1992",

month = jul,

doi = "10.1016/0165-2125(92)90046-5",

language = "English (US)",

volume = "16",

pages = "57--64",

journal = "Wave Motion",

issn = "0165-2125",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Asymptotic equations for conservation laws of mixed type

AU - Brio, Moysey

AU - Hunter, John K.

N1 - Funding Information: The work of M. Brio was partiallys upported by the NSF under grant DMS-8902097a nd by the Arizona Center for MathematicaSl ciences AFOSR ContractF 49620-86-C013T0h. e work of J.K. Hunter was partiallys upportedb y the NSF underg rantD MS-9011548.

PY - 1992/7

Y1 - 1992/7

N2 - We derive canonical asymptotic equations for weakly nonlinear solutions of conservation laws of mixed type. When two real wave speeds coalesce and become complex, we obtain the transonic small disturbance equation which changes type from hyperbolic to elliptic. When the coefficient of the nonlinear term in the transonic small disturbance equation vanishes, we derive cubically nonlinear 2 × 2 asymptotic equations. These include canonical equations which are parabolic on a line in state space and strictly hyperbolic away from this line.

AB - We derive canonical asymptotic equations for weakly nonlinear solutions of conservation laws of mixed type. When two real wave speeds coalesce and become complex, we obtain the transonic small disturbance equation which changes type from hyperbolic to elliptic. When the coefficient of the nonlinear term in the transonic small disturbance equation vanishes, we derive cubically nonlinear 2 × 2 asymptotic equations. These include canonical equations which are parabolic on a line in state space and strictly hyperbolic away from this line.

UR - http://www.scopus.com/inward/record.url?scp=44049118544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44049118544&partnerID=8YFLogxK

U2 - 10.1016/0165-2125(92)90046-5

DO - 10.1016/0165-2125(92)90046-5

M3 - Article

AN - SCOPUS:44049118544

SN - 0165-2125

VL - 16

SP - 57

EP - 64

JO - Wave Motion

JF - Wave Motion

IS - 1

ER -

Asymptotic equations for conservation laws of mixed type

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this