Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations I: Linearized Analysis at Criticality
Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations I: Linearized Analysis at Criticality
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DOI：
10.1007/s00021-021-00582-2
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发表时间：
2021-03
影响因子：
1.3
通讯作者：
Chun-Hsiung Hsia;Y. Kagei;T. Nishida;Y. Teramoto
中科院分区：
文献类型：
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作者：
Chun-Hsiung Hsia;Y. Kagei;T. Nishida;Y. Teramoto
双扩散对流方程的奇摄动系统（称为人工可压缩系统）在二维无限层上考虑，其参数范围在相应的不可压缩系统中发生 Hopf 分岔。详细研究了奇异摄动参数较小时时间周期函数空间中线性化算子在分岔点附近的谱。本文的结果是研究非线性Hopf分岔问题和时间周期分岔解的奇异极限的基础。
A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer for a parameters range where the Hopf bifurcation occurs in the corresponding incompressible system. The spectrum of the linearized operator in a time periodic function space is investigated in detail near the bifurcation point when the singular perturbation parameter is small. The results of this paper are the basis of the study of the nonlinear Hopf bifurcation problem and the singular limit of the time periodic bifurcating solutions.