Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations II: Bifurcation and Stability
Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations II: Bifurcation and Stability
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DOI：
10.1007/s00021-021-00583-1
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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
当不可压缩系统发生从静止状态的Hopf分叉时，考虑了双扩散对流系统从人工可压缩系统到不可压缩系统的奇摄动问题。证明了对于称为人工马赫数的小奇异摄动参数，人工可压缩系统也存在Hopf分叉。在人工马赫数为零的奇异极限下，证明了人工可压缩系统的时间周期解分支收敛到不可压缩系统的相应分支。
A singular perturbation problem from the artificial compressible system to the incompressible system is considered for a doubly diffusive convection when a Hopf bifurcation from the motionless state occurs in the incompressible system. It is proved that the Hopf bifurcation also occurs in the artificial compressible system for small singular perturbation parameter, called the artificial Mach number. The time periodic solution branch of the artificial compressible system is shown to converge to the corresponding bifurcating branch of the incompressible system in the singular limit of vanishing artificial Mach number.