On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains
On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains
复制标题
有界域中sinh-Gordon方程和N阶Toda系统的爆炸解的边界行为
DOI：
10.1093/imrn/rny263
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发表时间：
2020
影响因子：
1
通讯作者：
Yang Wen
中科院分区：
文献类型：
--
作者：
Ao Weiwei;Jevnikar Aleks;Yang Wen
本文研究了数学物理中有界区域上的两类问题：sinh-Gordon方程和一般秩n$户田系统的爆破分析。在爆破极限的剩余质量的存在下，使分析相当微妙，然而，通过利用适当的Pohozaev恒等式和详细的爆破分析，我们排除了在边界爆破。这是在存在残留质量的情况下，该方向的第一个结果。作为一个副产品，我们得到一般存在性结果在有界域。
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.