一个新的推广两分量Camassa-Holm 系统的持久性

Persistence Properties for a New Generalized Two-component Camassa-Holm-type System

解的长时间行为是偏微分方程研究中的一个重要问题.在很大程度上,解的性质取决于初值的性质.持久性指当初值满足无穷远处衰减的条件,则方程的解在无穷远处也衰减.在本文中,我们利用权函数估计的方法研究了一个新的推广两分量Camassa-Holm系统初值问题解的持久性,进而给出了最优衰减估计.

The long time behavior of solutions is one of important problems in the study of partial differential equations.To a great degree,the properties of solutions will depend on those of initial values.The persistence properties imply that the solutions of the equations decay at infinity when the initial data satisfies the condition of decaying at infinity.In this paper,we consider the persistence properties of solutions to the initial value problem for a new generalized two-component Camassa-Holmtype system by using weight functions.Furthermore,we give an optimal decaying estimate.