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
DOI: 10.12677/AAM.2023.126302, PDF, HTML, 下载: 103  浏览: 131 
作者: 蔡森林：重庆师范大学数学科学学院，重庆
关键词: 柯西问题；非一致连续性；浅水波模型；Cauchy Problem； Nonuniform Continuity； Shallow Water Wave
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。
Abstract: 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.
文章引用：蔡森林. 一类浅水波方程周期的非一致连续性[J]. 应用数学进展, 2023, 12(6): 3011-3020. https://doi.org/10.12677/AAM.2023.126302

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