Stability and bifurcation of traveling wave solutions
Stability and bifurcation of traveling wave solutions in a general one space dimension two-phase nonlinear free boundary problem are investigated by studying a family of differential equations in Banach spaces. Using invariant manifold and invariant foliation theories in infinite dimensional Banach spaces, a complete discussion on the stability of a family of equilibria for an ordinary differential equation in a Banach space is given. A new Hopf type bifurcation is found. It is shown that a one-parameter family of equilibria bifurcates into pieces of cylindrical type surface with spiral flows. For bifurcations from traveling wave solutions of general one space dimension two-phase free boundary problems, the bifurcating cylindrical type surface pieces from the traveling wave solutions connect together in a smooth way. Moreover, the flow on the global connected surface winds around with a periodic speed. Applications to a condensed two-phase combustion model are also discussed.
- Research Organization:
- Georgia Inst. of Tech., Atlanta, GA (United States)
- OSTI ID:
- 7204371
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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