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2010年09月30日

【期刊论文】WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR THE 2-COMPONENT CAMASSA-HOLM EQUATION

殷朝阳， Joachim Escher， Olaf Lechtenfeld， Zhaoyang Yin

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume 19, Number 3, November 2007，-0001，（）：

-1年11月30日

After some remarks on a possible zero-curvature formulation we first establish local well-posedness for the 2-component Camassa-Holm equation. Then precise blow-up scenarios for strong solutions to the system are derived. Finally we present two blow-up results for strong solutions to the system.

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2010年09月30日

【期刊论文】Global Solutions to a New Integrable Equation with Peakons

殷朝阳， ZHAOYANG YIN

Indiana University Mathematics Journal©, Vol.53, No.4 (2004)，-0001，（）：

-1年11月30日

摘要

We prove the existence and uniqueness of global strong solutions and global weak solutions for a new integrable equation with peakons.

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2010年09月30日

【期刊论文】ON THE STRUCTURE OF SOLUTIONS TO THE PERIODIC HUNTER-SAXTON EQUATION*

殷朝阳， ZHAOYANG YIN†

SIAM J. MATH. ANAL. Vol.36, No.1, pp.272-283，-0001，（）：

-1年11月30日

摘要

We prove the local existence of strong solutions of the periodic Hunter-Saxton equation, and we show that all strong solutions except space-independent solutions blow up in finite time.

local existence of strong solutions,， Hunter-Saxton equation,， blow-up of strong solutions

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2010年09月30日

【期刊论文】Global weak solutions and blow-up structure for the Degasperis-Procesi equation

殷朝阳， Joachim Escher a， Yue Liu b， Zhaoyang Yin a， c， *

Journal of Functional Analysis 241 (2006) 457-485，-0001，（）：

-1年11月30日

摘要

In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.

Degasperis-Procesi equation， Global weak solutions， Blow-up rate， Blow-up set