Date of Award:
Doctor of Philosophy (PhD)
Mathematics and Statistics
We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion.
The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence results can be applied. We then show that as the bifurcation parameter r decreases and passes through a critical value rc, the stationary solution loses stability and a stable periodic solution appears. Several figures have been included, which illustrate this transistion. The pascal source program used in the numerical simulation is included in an appendix.
Lee, Yoon-Mee, "Hopf Bifurcation in a Parabolic Free Boundary Problem" (1992). All Graduate Theses and Dissertations. 7138.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .