## Advances in Differential Equations

### On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions

Takeshi Isobe

#### Abstract

Let $\Omega\subset\mathbb R^2$ be a bounded domain, $\gamma\in C^{3,\alpha}(\partial\Omega;\mathbb R^3 )$ $(0 <\alpha <1)$ and $H>0$. We consider the asymptotic behavior of large solutions of an $H$-system $$\Delta u=2Hu_{x_1}\wedge u_{x_2}\quad\text{in \Omega}, \qquad u=\gamma\quad \text{on \partial\Omega}$$ as $H\to 0$ or as $\gamma\to 0$. We show that large solutions blow up at exactly one point in $\Omega$. The exact blow-up rate and location of blow-up point are studied.

#### Article information

Source
Adv. Differential Equations Volume 6, Number 5 (2001), 513-546.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
Isobe, Takeshi. On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions. Adv. Differential Equations 6 (2001), no. 5, 513--546.https://projecteuclid.org/euclid.ade/1357141854