双扩散对流方程Hopf分支的奇异极限Ⅰ：临界点的线性化分析
Singular limit in Hopf bifurcation for doubly diffusive convection equations I: linearized analysis at criticality
摘要：
研究了二维无限层上双扩散对流方程的奇异摄动系统（称为人工可压缩系统），在一定的参数范围内，相应的不可压缩系统发生Hopf分支.当奇异扰动参数较小时，详细研究了线性化算子在时间周期函数空间中的谱。本文的结果是研究非线性Hopf分支问题和时间周期分支解的奇异极限的基础。
英文摘要：
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.
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