On homogenization of a multidimensional diffusion with semipermeable reflecting interfaces
bk21
129동 301호
0
1618
2025.09.04 11:24
| 구분 | 초청강연 |
|---|---|
| 일정 | 2025-09-22(월) 15:00~16:00 |
| 세미나실 | 129동 301호 |
| 강연자 | Olga Ariasova (University of Jena and National Academy of Sciences of Ukraine) |
| 담당교수 | Gerald Trutnau |
| 기타 |
The mathematical problem of homogenization typically involves studying the effective parameters of a system that exhibits rapid variations in its spatial characteristics. However, we focus on a stochastic multivariate homogenization problem of a different kind: the diffusion in the presence of narrowly located semipermeable interfaces. In simple words, our model reminds of a foiled composite material consisting of a media interlaced with very thin plates of different permeability. In material science such models are referred to as reinforced materials like a glass wool reinforced by aluminium foil. Usually, one is interested in the effective parameters of such a system. By combining the study of stochastic differential equations with local times and homogenization, we explore how the presence of interfaces can alter the diffusion behavior of the limit process.
As a byproduct of our research, we obtain theorems for the existence and uniqueness of solutions to SDEs for multidimensional diffusion processes with membranes. Uniqueness is a problem of particular interest because it implies the strong Markov property of the solution, which is essential for the proof of convergence.
