Dear Colleagues,
We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi:
*Homogenization of a multivariate diffusion with semipermeable reflecting interfaces* by Olga Ariasova (Inst. Geophys. Nat. Acad. Sciences of Ukraine, F. Schiller Univ. of Jena)
The seminar will take place tomorrow TUE, 11.2.2025 at 14:00 CET in Aula Seminari, Dipartimento di Matematica, UNIPI and streamed online at the link below.
The organizers, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass
*---------------------------------------------------------* *Abstract: * 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.