Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations I: Linearized Analysis at Criticality

A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer parameters range where Hopf bifurcation occurs in corresponding incompressible system. The spectrum of linearized operator time periodic function space investigated detail near point when singular perturbation parameter small. results this paper are basis study nonlinear problem and limit bifurcating solutions.