一类非局部色散方程解的指数衰减性  

On exponential decay properties of the solutions to a class of nonlocal dispersive equations

作　　者：种鸽子 付英 CHONG Gezi;FU Ying(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2024年第2期234-246,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(11471259);陕西省自然科学基金(2019JM-007,2020JC-37);山西省自然科学基金(20210302124259)。

摘　　要：结合短波长尺度的物理学,本文讨论了一类非局部色散波动方程.首先,给出了该类稳态的非局部色散波动方程的孤立波解的指数型衰减性的相关结果,将单个方程指数衰减性的研究扩展到了一类方程,这是非常有意义的.其次,基于相关方程的柯西问题的局部适定性结果,研究了当初值在无穷远处衰减时该初值问题的强解的持久性性质.Considered herein is a class of nonlocal dispersive wave equations, which incorporates physics of short wavelength scales. At first, we give the results with respect to decay property of exponential type of its solitary solutions to the class steady nonlocal dispersive equations. It is of great interest to extend the study of the decay property of a single equation to a class of equations. Then, based on the local well-posedness results of the Cauchy problem associated with the equations, we investigate the persistence properties of the strong solution to this problem, provided the initial data decays at infinity.

关 键 词：一类非局部色散方程 孤立波解 指数衰减 持久性 

分 类 号：O175.29[理学—数学]