广义D-P类方程在有界域上的初边值问题
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摘要
证明了广义D-P类方程的局部解、整体解的存在性,并给出了广义D-P类方程局部解、整体解存在的充分条件.对解的性质进行了讨论,得到了相应的结果.
The paper proved the existence of local solution of initial value problem for D-P equation.The global solution existence of initial value problem for the equation was also proved by priorestimations.Give the academic elements for the application of D-P equation in elastic material.
The paper proved the existence of local solution of initial value problem for D-P equation.The global solution existence of initial value problem for the equation was also proved by priorestimations.Give the academic elements for the application of D-P equation in elastic material.
引文
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[7]KATO T.Quasi-linear equations of evolution with applications to partial differential equations[C]//Lecture Notes in Mathematics448.Berlin:Springer,2006:25-70.
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[2]DEGASPERIS A,HOLM D D,HONE A N W.A new integrableequation with peakon soiotons[J].Theory Math Phys,2002(4):1 461-1 472.
[3]HANS L,JACEK S.Multi-peakon solutions of the Degasperis-Procesiequation[J].Inverse Problems,2003(3):1 241-1 245.
[4]YIN Z Y.Global existence for a new periodic integrable equation.[J].Jounal of Math Analysis and Applications,2003(1):182-194.
[5]DAI H H.Model equation for nonilinear dispersive wave in a compressible Mooney-Rivilin rod[J].Acta Mech,1998,127:193-207.
[6]杨灵娥,郭柏灵.浅水波方程的初边值问题[J].数学理论与应用,2003(1):1-10.
[7]KATO T.Quasi-linear equations of evolution with applications to partial differential equations[C]//Lecture Notes in Mathematics448.Berlin:Springer,2006:25-70.
[8]KATO T.On the Cauchy problem for the generalized Kdv equation[J].Studies in Applied Mathematics,Advances in Mathematics,Supplementary Studies,1983(8):93-128.