Analytic Semigroup Approach To Higher Order Parabolic Problems

The subject of this book is to apply the analytic semigroup theory to solve various kinds of fourth order problems. In Chapter 2, we study the Cauchy problem for the surface diffusion flow and the Willmore flow in one dimensional case. In particular, we focus our attention to relax the regularity assumption on the initial curve. In Chapter 3, we extend the results of Chapter 2 for multi-dimensional case of various kinds of fourth order parabolic equations via maximal regularity. In the last Chapter, we consider the self-similar solution for the surface diffusion flow with boundary conditions.