Off-campus WSU users: To download campus access dissertations, please use the following link to log into our proxy server with your WSU access ID and password, then click the "Off-campus Download" button below.
Non-WSU users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
A Bifurcation Phenomenon Of Regularized Free Boundary Problems Of Two-Phase Elliptic-Parabolic Type
Date of Award
In this thesis, we prove that a bifurcation phenomenon exists in a two-phase singularly perturbed free boundary problem of phase transition. This extends the current knowledge for the one-phase problem. More precisely, the uniqueness of a solution of the two-phase problem breaks down as the boundary data decreases through a threshold value. The minimizer of the functional under consideration separates from the harmonic solution which is treated as a trivial solution in the absence of a free boundary. Moreover, we prove a third solution, a critical point of the functional being minimized, exists in this case by using the Mountain Pass Lemma. We prove convergence of the evolution with initial data, near a stable critical point to the stable solution, while the evolution deviates away from a saddle point solution of the free boundary problem as time goes by.
Raihen, Md Nurul Islam, "A Bifurcation Phenomenon Of Regularized Free Boundary Problems Of Two-Phase Elliptic-Parabolic Type" (2022). Wayne State University Dissertations. 3648.