PhD Dissertation Defense - Nurul Raihen

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Date: June 30, 2022
Time: 10:00 a.m. - 11:00 a.m.
Location: Virtual event
Category: Lecture

Speaker:

Nurul Raihen, PhD Candidate

Title: 

A bifurcation Phenomenon of Regularized Free Boundary Problems of Two-Phase Elliptic-Parabolic Type

Abstract: 

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.

Contact

Department of Mathematics
313-577-2479
math@wayne.edu

Cost

Free
June 2022
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