有界域和半无界域上广义Kawahara方程的初边值问题

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 57-71.

有界域和半无界域上广义Kawahara方程的初边值问题

卢美虹, 米彩莲, 杨晗

西南交通大学数学学院,四川成都,611756

出版日期:2016-12-30 发布日期:2020-09-27
基金资助:
国家自然科学基金项目(71572156,11501395)

Initial Boundary Value Problem to a Generalized Kawahara Equation on a Bounded Interval or a Half-line

Lu Meihong, Mi Cailian, Yang Han

School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China

Online:2016-12-30 Published:2020-09-27

摘要/Abstract

摘要： 本文在有界区域和半无界区域上研究广义Kawahara方程的初边值问题,运用能量积分方法､不等式技巧和嵌入定理建立解的先验估计,结合压缩映射原理证明了在有界区域上整体正则解的存在性和唯一性;同时得到当时间趋于无穷时,解的L2 范数具有指数衰减性;并且在加强的初边值条件下,借助不等式技巧证得在有界区域上存在与有界域长度无关的整体正则解,以及在半无界域上同样存在唯一的整体正则解.

关键词: 广义Kawahara方程, 整体正则解, 存在性, 唯一性

Abstract:

In this paper,we study the initial-boundary value problem to a generalized Kawahara equation on a bounded interval or a half-line.The energy integral method,the inequality technique and the embedding theorem are used to establish a prior estimate of the solution,and the existence and uniqueness of the global regular solution on a bounded interval are showed by the principle of contraction mapping.It is proved that the L2-norm of the solution has exponential decay when the time tends to infinity. Furthermore,under a stronger condition on the initial boundary values,the existence of a global regular solution on a bounded interval which is independent of the length of the bounded domain,and the existence of a unique global regular solution on a half

-line are derived.

Key words: Generalized Kawahara equation, Global regular solution, Existence, Uniqueness

卢美虹, 米彩莲, 杨晗. 有界域和半无界域上广义Kawahara方程的初边值问题[J]. 数学理论与应用, 2016, 36(4): 57-71.

Lu Meihong, Mi Cailian, Yang Han.

Initial Boundary Value Problem to a Generalized Kawahara Equation on a Bounded Interval or a Half-line [J]. Mathematical Theory and Applications, 2016, 36(4): 57-71.