Rough Boundaries in Thin Domains with Signorini Constraints
Miércoles 28/5, 11.30h
Seminario
El Departamento de Matemáticas y Estadística de la Universidad Torcuato Di Tella invita al seminario “Rough Boundaries in Thin Domains with Signorini Constraints”, a cargo de Marcone Corrêa Pereira.
Abstract
In this presentation, we explore a reaction-diffusion problem within a thin planar domain, subject to a Signorini-type boundary condition that models boundary-catalyzed reactions. Motivated by applications in microfluidics and free-boundary problems, we consider scenarios where the boundary exhibits resonant roughness—meaning the amplitude and period of the surface irregularities are on the same scale as the domain’s thickness. Depending on the intensity of the reaction mechanism governed by the Signorini condition, we identify three distinct behavioral regimes. Notably, we highlight the critical regime in which the influence of the domain’s geometry and all physically relevant aspects of the process are fully captured.
This is a collaborative work with Prof. Antonio Gaudiello (Università degli Studi della Campania Luigi Vanvitelli) and Jean Carlos Nakasato (IME-USP).
Marcone Corrêa Pereira. Full Professor in the Department of Mathematics at IME-USP. His research focuses on Dynamical Systems—particularly their attractors under perturbations—and Partial Differential Equations. Since completing his Ph.D. in 2004, he has held extended research visits at institutions such as Universidad Complutense de Madrid, University of Minnesota, Universidad de Buenos Aires, and Pontifícia Universidad Católica de Chile. Professor Pereira has published numerous articles in leading international journals, including Mathematische Annalen, Journal of Differential Equations, Advanced Nonlinear Studies, Bulletin of the London Mathematical Society, and Journal de Mathématiques Pures et Appliquées. He has supervised two Ph.D. theses and several postdoctoral researchers. Since 2020, he has held the prestigious Bolsista de Produtividade em Pesquisa (PQ1D level) distinction awarded by CNPq.
Abstract
In this presentation, we explore a reaction-diffusion problem within a thin planar domain, subject to a Signorini-type boundary condition that models boundary-catalyzed reactions. Motivated by applications in microfluidics and free-boundary problems, we consider scenarios where the boundary exhibits resonant roughness—meaning the amplitude and period of the surface irregularities are on the same scale as the domain’s thickness. Depending on the intensity of the reaction mechanism governed by the Signorini condition, we identify three distinct behavioral regimes. Notably, we highlight the critical regime in which the influence of the domain’s geometry and all physically relevant aspects of the process are fully captured.
This is a collaborative work with Prof. Antonio Gaudiello (Università degli Studi della Campania Luigi Vanvitelli) and Jean Carlos Nakasato (IME-USP).
Marcone Corrêa Pereira. Full Professor in the Department of Mathematics at IME-USP. His research focuses on Dynamical Systems—particularly their attractors under perturbations—and Partial Differential Equations. Since completing his Ph.D. in 2004, he has held extended research visits at institutions such as Universidad Complutense de Madrid, University of Minnesota, Universidad de Buenos Aires, and Pontifícia Universidad Católica de Chile. Professor Pereira has published numerous articles in leading international journals, including Mathematische Annalen, Journal of Differential Equations, Advanced Nonlinear Studies, Bulletin of the London Mathematical Society, and Journal de Mathématiques Pures et Appliquées. He has supervised two Ph.D. theses and several postdoctoral researchers. Since 2020, he has held the prestigious Bolsista de Produtividade em Pesquisa (PQ1D level) distinction awarded by CNPq.