# PhD Dissertation Defense - Nurul Raihen

This event is in the past.

**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