TY - JOUR
T1 - Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations I
T2 - Linearized Analysis at Criticality
AU - Hsia, Chun Hsiung
AU - Kagei, Yoshiyuki
AU - Nishida, Takaaki
AU - Teramoto, Yuka
N1 - Funding Information:
C.-H. Hsia was partly supported by NCTS and MOST Grant 109-2115-M-002-013-MY3. Y. Kagei was partly supported by JSPS KAKENHI Grant Numbers 16H03947, 16H06339 and 20H00118. T. Nishida is partly supported by JSPS KAKENHI Grant Number 20K03699.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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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U2 - 10.1007/s00021-021-00582-2
DO - 10.1007/s00021-021-00582-2
M3 - Article
AN - SCOPUS:85105631279
SN - 1422-6928
VL - 23
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
IS - 3
M1 - 60
ER -