一类浅水波方程周期的非一致连续性  

Nonuniform Continuity of a Class of Shallow Water Wave Equation

作　　者：蔡森林 

机构地区：[1]重庆师范大学数学科学学院,重庆

出　　处：《应用数学进展》2023年第6期3011-3020,共10页Advances in Applied Mathematics

摘　　要：本文研究中等振幅浅水波模型的周期柯西问题,我们首先构造了两个解序列,他们在Hs(T), s > 3/2中是有界的,并且在初值时刻区间收敛到零,但是这两个序列之间的距离的下界在任意时刻T是一个非零常数,这意昧着方程的解映射在Sobolev空间中是非一致连续的。In this paper, the periodic Cauchy problem of shallow water wave model with moderate Hs(T), s > 3/2, and converge to zero at the initial time interval, but the bound of the distance between these two sequence is a non-zero constance at any time. This means that the solution mapping of the equation is non-uniformly continuous in Sobolev space.

关 键 词：柯西问题 非一致连续性 浅水波模型 

分 类 号：O17[理学—数学]