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【期刊论文】Initial Boundary Value Problems of the Camassa-Holm Equation
殷朝阳, JOACHIM ESCHER AND ZHAOYANG YIN
Communications in Partial Differential Equations, 33: 377-395, 2008,-0001,():
-1年11月30日
In this paper we study initial boundary value problems of the Camassa-Holm equation on the half line and on a compact interval. Using rigorously the conservation of symmetry, it is possible to convert these boundary value problems into Cauchy problems for the Camassa-Holm equation on the line and on the circle, respectively. Applying thus known results for the latter equations we first obtain the local well-posedness of the initial boundary value problems under consideration. Then we present some blow-up and global existence results for strong solutions. Finally we investigate global and local weak solutions for the equation on the half line and on a compact interval, respectively. An interesting result of our analysis shows that the Camassa-Holm equation on a compact interval possesses no nontrivial global classical solutions.
Blow-up and global existence, Global weak solutions, Initial boundary value problems, Local well-posedness, The Camassa-Holm equation.,
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【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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【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
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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【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
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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【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
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
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