Interface dynamics focuses on how boundaries between different states evolve over time. We study processes such as mixing of materials and the spontaneous formation of patterns, exploring the rules that govern their behavior.
Variational methods offer a framework for finding the natural state of a system via energy minimization. The resulting PDEs then describe interface motion and shape evolution, enabling a unified, quantitative understanding of complex phenomena.
Partial Differential Equations (PDEs) provide a mathematical framework for describing phenomena that change over time and space. In our lab, we study processes such as diffusion, wave propagation, and interface motion to better understand the underlying mechanisms of these phenomena.
Computational simulation is a method for reproducing mathematical models on a computer to visualize and analyze complex phenomena. In our lab, we combine theory and computation to study interface motion and free boundary problems, deepening our understanding of their dynamics.