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Volume 12, Issue 1
A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition

YoonMee Ham

J. Part. Diff. Eq., 12 (1999), pp. 71-84.

Published online: 1999-12

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  • Abstract
In this paper, we consider the free boundary problem satisfying the Dirichlet boundary condition. This problem is derived from the reaction diffusion equations with the generalized McKean reaction dynamics. We shall show a Hopf bifurcation occurs at some critical point τ when the stationary solution (v^⋅ (x), s^⋅) satisfies 1/3 < s^⋅ < 1.
  • Keywords

Evolution equation free boundary problem Hopf bifurcation internal layer solution parabolic equation

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@Article{JPDE-12-71, author = {YoonMee Ham }, title = {A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition}, journal = {Journal of Partial Differential Equations}, year = {1999}, volume = {12}, number = {1}, pages = {71--84}, abstract = { In this paper, we consider the free boundary problem satisfying the Dirichlet boundary condition. This problem is derived from the reaction diffusion equations with the generalized McKean reaction dynamics. We shall show a Hopf bifurcation occurs at some critical point τ when the stationary solution (v^⋅ (x), s^⋅) satisfies 1/3 < s^⋅ < 1.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5526.html} }
TY - JOUR T1 - A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition AU - YoonMee Ham JO - Journal of Partial Differential Equations VL - 1 SP - 71 EP - 84 PY - 1999 DA - 1999/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5526.html KW - Evolution equation KW - free boundary problem KW - Hopf bifurcation KW - internal layer solution KW - parabolic equation AB - In this paper, we consider the free boundary problem satisfying the Dirichlet boundary condition. This problem is derived from the reaction diffusion equations with the generalized McKean reaction dynamics. We shall show a Hopf bifurcation occurs at some critical point τ when the stationary solution (v^⋅ (x), s^⋅) satisfies 1/3 < s^⋅ < 1.
YoonMee Ham . (1999). A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition. Journal of Partial Differential Equations. 12 (1). 71-84. doi:
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