The Cahn-Hilliard equation is a celebrated diffuse interface (phase field) model proposed in material sciences to describe phase separation in binary alloys. It is nowadays widely used in fluid mechanics, biology and image processing. The Cahn-Hilliard equation corresponds to the gradient flow associated with the Ginzburg-Landau free energy with Flory-Huggins potential subject to the mass conservation constraint. Although the global well-posedness is by now well-known, some questions concerning the regularity of the solutions and the so-called separation property remain unsolved. In this talk, I will discuss some open problems and partial answers for local and nonlocal Cahn-Hilliard equations.  > 本报告受到复旦大学高等学术研究院“Fudan Fellow”项目资助。

学术报告海报202311205Giorgini.pdf