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Ham, Yoon-Mee Korean Mathematical Society 1999 대한수학회논문집 Vol.14 No.2
A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.
GLOBAL COUPLING EFFECTS ON A FREE BOUNDARY PROBLEM FOR THREE-COMPONENT REACTION-DIFFUSION SYSTEM
Ham, Yoon-Mee Korean Mathematical Society 2006 대한수학회지 Vol.43 No.3
In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.
A GLOBALITY OF A HOPF BIFURCATION IN A FREE BOUNDARY PROBLEM
Ham, Yoon-Mee Korean Mathematical Society 1997 대한수학회지 Vol.34 No.2
A globality of the Hopf bifurcation in a free boundary problem for a parabolic partial differential equation is investigated in this paper. We shall examine the global behavior of the Hopf critical eigenvalues and and apply the center-index theory to show the globality.
Hopf bifurcation in an interface problem with McKean relaxation oscillators
Ham, Yoon-Mee 경기대학교 사회과학연구소 2005 경기대학교 기초과학논문집 Vol.18 No.1
We shall consider an interfacial problem arising reaction-diffusion models with McKean relaxation oscillator. The purpose of this paper is to analyze the occurrence of Hopf bifurcation in the interfacial problem and to examine the effects of an inhomogeneous media. Conditions for existence of stationary solutions and Hopf bifurcation for a certain class of inhomogeneity are obtained analytically.
A hopf bifurcation on a parabolic free boundary problem with pushchino dynamics
Ham, Yoon-Mee,Seung, Byong-In Korean Mathematical Society 1995 대한수학회지 Vol.32 No.2
A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).
Ham, Yoon-Mee Korean Mathematical Society 1999 대한수학회보 Vol.36 No.4
In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).
A Linearlization of a Free Boundary Problem with the Generalized Mckean Kinetics
Lee, Sang-Gu,Ham, Yoon-Mee 성균관대학교 기초과학연구소 1993 論文集 Vol.44 No.2
비선형 자유 경계치 문제에 대하여 그 해의 asymtotic behavior를 연구하는데 있어서는 대부분 그 문제를 선형화 시켜서 그 선형부분을 연구하는 것으로 충분하다. 이 논문에서는 generalized Mckean kinetics 항을 갖는 자유경계치 문제를 linearized eigenvalue 문제로 바꾼다. 이것은 해의 존재성과 bifurcation등을 보이는데 바로 이용된다.