A mixed boundary value problem for Chaplygin's hodograph equation

Li Liu; Meng Xu; Hairong Yuan

doi:10.1016/j.jmaa.2014.09.075

A mixed boundary value problem for Chaplygin's hodograph equation

Li Liu
, Meng Xu^*
, Hairong Yuan

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai University of International Business and Economics
Nanjing University of Science and Technology

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

4 Scopus citations

Abstract

In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations.

Original language	English
Pages (from-to)	60-75
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	423
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.09.075
State	Published - 2015

Keywords

Chaplygin's equation
Degenerate elliptic equation
Existence
Perron's method
Uniqueness

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10.1016/j.jmaa.2014.09.075

Cite this

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title = "A mixed boundary value problem for Chaplygin's hodograph equation",

abstract = "In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations.",

keywords = "Chaplygin's equation, Degenerate elliptic equation, Existence, Perron's method, Uniqueness",

author = "Li Liu and Meng Xu and Hairong Yuan",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

doi = "10.1016/j.jmaa.2014.09.075",

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volume = "423",

pages = "60--75",

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T1 - A mixed boundary value problem for Chaplygin's hodograph equation

AU - Liu, Li

AU - Xu, Meng

AU - Yuan, Hairong

PY - 2015

Y1 - 2015

N2 - In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations.

AB - In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations.

KW - Chaplygin's equation

KW - Degenerate elliptic equation

KW - Existence

KW - Perron's method

KW - Uniqueness

UR - https://www.scopus.com/pages/publications/84923004903

U2 - 10.1016/j.jmaa.2014.09.075

DO - 10.1016/j.jmaa.2014.09.075

M3 - 文章

AN - SCOPUS:84923004903

SN - 0022-247X

VL - 423

SP - 60

EP - 75

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A mixed boundary value problem for Chaplygin's hodograph equation

Abstract

Keywords

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