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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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【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】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】On the stability ofequilibria to weakly coupled parabolic systems in unbounded domains
殷朝阳, Joachim Escher a, *, ZhaoyangYin b
Nonlinear Analysis 60 (2005) 1065-1084,-0001,():
-1年11月30日
We investigate weakly coupled semilinear parabolic systems in unbounded domains of R2 or R3 with general nonlinearities.We present several sufficient conditions on the nonlinearities which ensure the stability ofthe zero solution with respect to H2-perturbations. In addition, various examples are discussed to illustrate the scope ofapplication ofour results.
Stable equilibria, Parabolic systems, Unbounded domains
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