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【期刊论文】Shock Waves and Blow-up Phenomena for the Periodic Degasperis-Procesi Equation
殷朝阳, JOACHIM ESCHER, YUE LIU & ZHAOYANG YIN
Indiana University Mathematics Journal©, Article electronically published on January 30, 2007,-0001,():
-1年11月30日
In this paper we mainly study the problem of the development of singularities for solutions to the periodic Degasperis-Procesi equation. Firstly, we show that the first blow-up of strong solution to the equation must occur only in the form of wave breaking and shock waves possibly appear afterwards. Secondly, we established two new blow-up results. Thirdly, we investigate the blow-up rate for all non-global strong solutions and determine the blow-up set of blowing-up strong solutions to the equation for a large class of initial data. We finally give an explicit example of weak solutions to the equation, which may be considered as periodic shock waves.
the periodic Degasperis-Procesi equation, periodic peakons, periodic shock waves, blow-up rate, blow-up set
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【期刊论文】Global solutions for quasilinear parabolic systems
殷朝阳, Adrian Constantin, a, Joachim Escher, b and Zhaoyang Yin c
J. Differential Equations 197 (2004) 73-84,-0001,():
-1年11月30日
We present an approach for proving the global existence of classical solutions of certain quasilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary.
Global solutions, Quasilinear parabolic systems, Dirichlet condition
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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】Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation
殷朝阳, Yue Liu, Zhaoyang Yin,
Commun. Math. Phys. 267, 801-820 (2006),-0001,():
-1年11月30日
This paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the Degasperis-Procesi equation on the line. Global strong solutions to the equation are determined for a class of initial profiles. On the other hand, it is shown that the first blow-up can occur only in the form of wavebreaking. A new wave-breaking mechanism for solutions is described in detail and two results of blow-up solutions with certain initial profiles are established.
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