四川大学学报（自然科学版）2026，Vol.63Issue(2)：323-327,5.DOI:10.19907/j.0490-6756.240207
拟周期驱动Boussinesq方程响应解的存在性
Existence of response solutions of quasi-periodically forced Boussinesq equations
摘要
Abstract
In this paper,the existence of response solutions of the following Boussinesq equation with quasi-periodic force term and hinged boundary condition is considered,{ytt(t,x)=μyxxxxx+yxx+(y3)xx+εf(ωt,x),x∈T͂=[0,π],y(t,0)=y(t,π)=yxx(t,0)=yxx(t,π)=0,where μ>1,f:Td×T͂→R,Td=(R\2πZ)d is quasi-periodic with respect to t,d≥2 is a natural number,ω=(ω1,ω2,…,ωd)∈Rd\{0}is rationally independent,ε is sufficiently small,For both analytic and highly differentiable force terms,the corresponding existences of response solutions of the equation are obtained.In comparison with the known results,we extend the two-dimensional frequency to finite dimension frequency,the analytic force term to highly differentiable force term.关键词
Boussinesq方程/响应解/压缩映射原理Key words
Boussinesq equation/response solution/contraction mapping principle分类
数理科学引用本文复制引用
杨莲,舒兴奎,王芬芬..拟周期驱动Boussinesq方程响应解的存在性[J].四川大学学报（自然科学版）,2026,63(2):323-327,5.基金项目
国家自然科学基金(12101434) （12101434）
四川省自然科学基金(24NSFSC4934) （24NSFSC4934）
