scholarly journals The blow up analysis of solutions of the elliptic sinh-Gordon equation

2007 ◽  
Vol 31 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Jürgen Jost ◽  
Guofang Wang ◽  
Dong Ye ◽  
Chunqin Zhou
Keyword(s):  
Gordon Equation ◽  
Blow Up ◽  
Blow Up Analysis

On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains

2018 ◽  
Vol 2020 (23) ◽  
pp. 9386-9419 ◽  
Author(s):  
Weiwei Ao ◽  
Aleks Jevnikar ◽  
Wen Yang
Keyword(s):  
Gordon Equation ◽  
Blow Up ◽  
Boundary Behavior ◽  
Bounded Domains ◽  
Residual Mass ◽  
Blow Up Analysis ◽  
Blowing Up ◽  
General Rank ◽  
General Existence ◽  
Toda Systems

Abstract In this paper we are concerned with the blow-up analysis of two classes of problems in bounded domains arising in mathematical physics: sinh-Gordon equation and some general rank $n$ Toda systems. The presence of a residual mass in the blowing up limit makes the analysis quite delicate; nevertheless, by exploiting suitable Pohozaev identities and a detailed blow-up analysis we exclude blowup at the boundary. This is the 1st result in this direction in the presence of a residual mass. As a byproduct we obtain general existence results in bounded domains.

BLOW-UP ANALYSIS FOR LIOUVILLE TYPE EQUATION IN SELF-DUAL GAUGE FIELD THEORIES

2005 ◽  
Vol 07 (02) ◽  
pp. 177-205 ◽  
Author(s):  
HIROSHI OHTSUKA ◽  
TAKASHI SUZUKI
Keyword(s):  
Gauge Field ◽  
Blow Up ◽  
Type Equation ◽  
Singular Part ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Liouville Type ◽  
Blow Up Analysis ◽  
The Green Function ◽  
Dirac Measures

We study the asymptotic behavior of the solution sequence of Liouville type equations observed in various self-dual gauge field theories. First, we show that such a sequence converges to a measure with a singular part that consists of Dirac measures if it is not compact in W1,2. Then, under an additional condition, the singular limit is specified by the method of symmetrization of the Green function.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

Blow-Up Analysis for Heat Flow of Harmonic Maps

Nematics ◽  
1991 ◽  
pp. 49-64
Author(s):  
Chen Yunmei ◽  
Ding Wei-Yue
Keyword(s):  
Heat Flow ◽  
Blow Up ◽  
Harmonic Maps ◽  
Blow Up Analysis
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