Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

被引：15

作者：

Han, Qing ^{[1
,2
]}

Khuri, Marcus ^{[3
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

[3] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 38卷 / 12期

基金：

美国国家科学基金会;

关键词：

Blow-up solutions; Generalized Jang equation; Penrose inequality; PROOF; TOPOLOGY; ENERGY;

D O I：

10.1080/03605302.2013.837919

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.

引用

页码：2199 / 2237

页数：39

共 50 条

[21] Global existence and blow-up solutions for a nonlinear shallow water equation
Liu, Yue
MATHEMATISCHE ANNALEN, 2006, 335 (03) : 717 - 735
[22] On the existence and blow-up of solutions for a mean field equation with variable intensities
Ricciardi, Tonia
Takahashi, Ryo
Zecca, Gabriella
Zhang, Xiao
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2016, 27 (04) : 413 - 429
[23] Blow-up and global existence of solutions for a time fractional diffusion equation
Yaning Li
Quanguo Zhang
Fractional Calculus and Applied Analysis, 2018, 21 : 1619 - 1640
[24] Global existence and blow-up of solutions for the heat equation with exponential nonlinearity
Fujishima, Yohei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) : 6809 - 6842
[25] Global existence and blow-up solutions for a nonlinear shallow water equation
Yue Liu
Mathematische Annalen, 2006, 335 : 717 - 735
[26] EXISTENCE AND BLOW-UP OF SOLUTIONS TO A PARABOLIC EQUATION WITH NONSTANDARD GROWTH CONDITIONS
Liu, Yang
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (02) : 242 - 249
[27] Global existence, asymptotic stability and blow-up of solutions for the generalized Boussinesq equation with nonlinear boundary condition
Zhang, Hongwei
Hu, Qingying
Liu, Gongwei
MATHEMATISCHE NACHRICHTEN, 2020, 293 (02) : 386 - 404
[28] Blow-up of solutions to the DGH equation
Zhou, Yong
JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 250 (01) : 227 - 248
[29] Asymptotic behavior and blow-up of solutions for the viscous diffusion equation
Xu Runzhang
APPLIED MATHEMATICS LETTERS, 2007, 20 (03) : 255 - 259
[30] Global existence and blow-up for Riccati equation
Zhang, WN
DYNAMIC SYSTEMS AND APPLICATIONS, 2003, 12 (3-4): : 251 - 258

← 1 2 3 4 5 →