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2001 On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions
Takeshi Isobe
Adv. Differential Equations 6(5): 513-546 (2001). DOI: 10.57262/ade/1357141854

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.

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Takeshi Isobe. "On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions." Adv. Differential Equations 6 (5) 513 - 546, 2001. https://doi.org/10.57262/ade/1357141854

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1142.35345
MathSciNet: MR1826720
Digital Object Identifier: 10.57262/ade/1357141854

Subjects:
Primary: 35B40
Secondary: 35J50 , 35J60

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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