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.
引文
[1]POPOWICZ Z.A 2-component generalization of the Degasperis-Procesi equation[J].Journal of Physics A:General Physics,2006,39(44):13717-13726.
[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.