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.

中文翻译：

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双扩散对流方程Hopf分支的奇异极限I：临界状态下的线性化分析

在二维无限层上考虑了在相应的不可压缩系统中发生Hopf分叉的参数范围，在二维无限层上考虑了一个用于双扩散对流方程的奇摄动系统，称为人工可压缩系统。当奇异摄动参数小时，在分岔点附近，详细研究时间周期函数空间中线性化算子的谱。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。