今後のセミナーの予定
Schedules of future seminars
● 2026 年 4 月 27 日 (Mon) 16:00 〜 17:00
- 講演者
- Ulisse Stefanelli 氏 （University of Vienna）
- 講演題目
- A free boundary problem in accretive growth
- 講演要旨
-
Accretive growth, in which material is added at the boundary of a system, is a central phenomenon in biology, natural processes, and engineering.
Mathematically, it can be described by a stationary Hamilton-Jacobi equation governing the motion of the boundary, coupled with a PDE for an activation field (such as nutrients, temperature, or stress) defined on the evolving domain.
This results in a free boundary problem with a highly nonlinear, coupled structure.
In this talk, I will present an existence analysis for such a problem.
I will begin with the growth subproblem, where I establish sharp regularity properties of the sublevel sets of the solution.
In particular, I will show that the growing domains satisfy a uniform Poincaré inequality.
This provides the analytical framework needed to prove an existence result for the fully coupled free boundary system.