A free boundary problem in accretive growth
김수현
27동 325호
0
40
02.17 21:47
| 구분 | 편미분방정식 |
|---|---|
| 일정 | 2026-02-25(수) 16:00~17:00 |
| 세미나실 | 27동 325호 |
| 강연자 | Ulisse Stefanelli (Univeristy of Vienna, Austria) |
| 담당교수 | 변순식 |
| 기타 |
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.
