Camassa-Holm方程与Degasperis-Procesi方程相互作用系统的持久性
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摘要
首先通过权函数估计法,研究了Camassa-Holm方程与Degasperis-Procesi方程相互作用系统初值问题解的持久性.其次推导了该初值问题解的最佳衰减指数.
The persistence properties of the initial value problem for the interacting system of the Camassa-Holm and Degasperis-Procesi equations are studied by using an estimate with weight function.Then the optimal decay index of the solutions to the system is derived.
The persistence properties of the initial value problem for the interacting system of the Camassa-Holm and Degasperis-Procesi equations are studied by using an estimate with weight function.Then the optimal decay index of the solutions to the system is derived.
引文
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[15]HENRY D.Persistence properties for the Degasperis-Procesi equation[J].Journal of Hyperbolic Differential Equations,2008,5(1):99-111.
[16]HU Q Y,QIAO Z J.Persistence properties and unique continuation for a dispersionless two-component Camassa-Holm system with peakon and weak kink solutions[J].Discrete and Continuous Dynamical Systems Series A,2016,36(5):2613-2625.
[2]POPOWICZ Z.A Camassa-Holm equation interacted with the Degasperis-Procesi equation[J].Czechoslovak Journal of Physics,2006,56(10):1263-1268.
[3]CAMASSA R,HOLM D D.An integrable shallow water equation with peaked solitons[J].Physical Review Letters,1993,71(11):1661-1664.
[4]DEGASPERIS A,HOLM D D,HONE ANW.A new integral equation with peakon solutions[J].Theoretical and Mathematical Physics,2002,133(2):1463-1474.
[5]LI Y,OLVER P.Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation[J].Journal of Differential Equations,2000,162(1):27-63.
[6]YIN Z.On the Cauchy problem for an integrable equation with peakon solutions[J].Illinois Journal of Mathematics,2003,47(2003):649-666.
[7]CONSTANTIN A,ESCHER J.Wave breaking for nonlinear nonlocal shallow water equations[J].Acta Mathematica,1998,181(2):229-243.
[8]ZHOU Y.Blow-up phenomena for the integrable DegasperisProcesi equation[J].Physics Letters-Section A,2004,328(2):157-162.
[9]FU Y,QU C Z.Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and DegasperisProcesi equations[J].Discrete and Continuous Dynamical Systems Series A,2012,27(3):1025-1035.
[10]WANG M X,YU S Q.An interacting system of the Camassa-Holm and Degasperis-Procesi equations[J].Journal of Mathematical Physics,2012,53(6):60-91.
[11]ZHOU S M.The local well-posedness in Besov spaces and non-uniform dependence on initial data for the interacting system of the Camassa-Holm and Degasperis-Procesi equations[J].Monatshefte Für Mathematik,2018,187(4):735-764.
[12]HIMONAS A A,MISIOL/EK G,PONCE G,et al.Persistence properties and unique continuation of solution of the Camassa-Holm equation[J].Communications in Mathematical Physics,2007,271(2):511-522.
[13]FU Y,QU C Z.Unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations[J].Acta Mathematica Scientia,2012,32(2):652-662.
[14]WU X L,GUO B L.Persistence properties and infinite propagation for the modified 2-component Camassa-Holm equation[J].Discrete and Continuous Dynamical Systems Series A,2013,33(7):3211-3223.
[15]HENRY D.Persistence properties for the Degasperis-Procesi equation[J].Journal of Hyperbolic Differential Equations,2008,5(1):99-111.
[16]HU Q Y,QIAO Z J.Persistence properties and unique continuation for a dispersionless two-component Camassa-Holm system with peakon and weak kink solutions[J].Discrete and Continuous Dynamical Systems Series A,2016,36(5):2613-2625.