分数阶Burgers方程时间周期弱解的唯一性与渐近稳定性  

Uniqueness and Asymptotic Stability of Time-Periodic Solutions for the Fractional Burgers Equation

作　　者：徐斐 张勇[2] Xu Fei;Zhang Yong(School of Mathematical Sciences,Jiangsu University,Jiangsu Zhenjiang 212013;Institute of Applied System Analysis,Jiangsu University,Jiangsu Zhenjiang 212013)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013 [2]江苏大学应用系统分析研究院,江苏镇江212013

出　　处：《数学物理学报（A辑）》2023年第6期1710-1722,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971202)。

摘　　要：该文主要讨论实轴上分数阶Burgers方程时间周期弱解的性质.首先利用伽辽金逼近和傅里叶展开的方法,得到了分数阶Burgers方程对应的线性化问题时间周期弱解的存在性.然后通过构造合适的压缩映射,得到了非线性方程时间周期弱解的存在唯一性,并进一步证明了该时间周期弱解是渐近稳定的.此外,该文中的方法也可以用来处理有界区间上的问题,并进一步提升了文献[5]中已有的结果.The paper is concerned with the time-periodic(T-periodic) problem of fractional Burgers equation on the real line.Based on the Galerkin approximates and Fourier expansion,we first prove the existence of T-periodic solution to a linearized version.Then,the existence and uniqueness of T-periodic solution for the nonlinear equation are established by constructing a suitable contraction mapping.Furthermore,we show that the unique T-periodic solution is asymptotically stable.In addition,our method can be extended to the classical forced Burgers equation in a bounded region,which improves the known result.

关 键 词：唯一性 分数阶 压缩映射 渐近稳定性 

分 类 号：O175[理学—数学]