MONOTONICITY AND UNIQUENESS OF A 3D TRANSONIC SHOCK SOLUTION IN A CONIC NOZZLE WITH VARIABLE END PRESSURE

被引：10

作者：

Li, Jun ^{[1
,2
]}

Xin, Zhouping ^{[3
,4
]}

Yin, Huicheng ^{[1
,2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[2] Nanjing Univ, Inst Math Sci, Nanjing 210093, Jiangsu, Peoples R China

[3] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[4] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2011年 / 254卷 / 01期

关键词：

steady Euler system; transonic shock; first-order elliptic system; index of Hilbert problem; maximum principle of weak solutions; EQUATIONS; DUCT;

D O I：

10.2140/pjm.2011.254.129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We focus on the uniqueness problem of a 3D transonic shock solution in a conic nozzle when the variable end pressure in the diverging part of the nozzle lies in an appropriate scope. By establishing the monotonicity of the position of shock surface relative to the end pressure, we remove the nonphysical assumptions on the transonic shock past a fixed point made in previous studies and further obtain uniqueness.

引用

页码：129 / 171

页数：43

共 26 条

[1]

[Anonymous], 1952, MAT SB

[2]

[Anonymous], 2002, BOUNDARY VALUE PROBL

[3] ON DIRICHLETS PROBLEM FOR ELLIPTIC-EQUATIONS IN SECTIONALLY SMOOTH N-DIMENSIONAL DOMAINS [J].

AZZAM, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1980, 11 (02) :248-253

[4]

Azzam A., 1981, ANN POL MATH, V1, P81

[5] PARTIAL DIFFERENTIAL EQUATIONS AND GENERALIZED ANALYTIC FUNCTIONS - 2ND NOTE [J].

BERS, L .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1951, 37 (01) :42-47

[6] PARTIAL DIFFERENTIAL EQUATIONS AND GENERALIZED ANALYTIC FUNCTIONS [J].

BERS, L .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1950, 36 (02) :130-136

[7]

Canic S, 2000, COMMUN PUR APPL MATH, V53, P484

[8] Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles [J].

Chen, Gui-Qiang ;

Chen, Jun ;

Feldman, Mikhail .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 88 (02) :191-218

[9] Transonic shocks in 3-D compressible flow passing a duct with a general section for Euler systems [J].

Chen, Shuxing .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (10) :5265-5289

[10] Transonic shocks in compressible flow passing a duct for three-dimensional Euler systems [J].

Chen, Shuxing ;

Yuan, Hairong .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2008, 187 (03) :523-556

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