Stability and Bifurcation Analysis of Applied Free Boundary Problems

Free boundary problems (the time dependent problems are also often known as moving boundary problems) deal with systems of partial differential equations (PDEs) where the domain boundary is apriori unknown. Many mathematical models in different disciplines, e.g., biology, ecology, physics, and material science, involve the formulation of free boundary problems. In this thesis, several free boundary problems with real-world applications are studied, which include a tumor growth model with a time delay in cell proliferation, a plaque formation model, and a modified Hele-Shaw problem. Stability and bifurcation analysis are presented to analyze these models. Each chapter is devoted to a separate mathematical model.