Boundary perturbation problems on partial differential equations

• Grant number: 22/08112-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2022
• End date: August 06, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcone Corrêa Pereira
• Grantee: Jean Carlos Nakasato
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/14075-6 - Dynamical systems and their attractors under perturbations, AP.TEM
• Associated scholarship(s): 23/03847-6 - Asymptotic analysis of differential equations in singularly perturbed domains, BE.EP.PD

Abstract

This project is associated with a request for a postdoctoral research grant for a period of approximately 2 years. In general terms, we propose to investigate issues related to the asymptotic and geometric analysis of parabolic equations in relation to the perturbation of the domain defining their solutions. Among so many, we intend to study models associated with boundary value problems on rough surfaces and thin channels. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

NAKASATO, JEAN CARLOS; PAZANIN, IGOR; PEREIRA, MARCONE CORREA. On the non-isothermal, non-Newtonian Hele-Shaw flows in a domain with rough boundary. Journal of Mathematical Analysis and Applications, v. 524, n. 1, p. 21-pg., 2023-02-07. (22/08112-1, 20/04813-0)

NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. A reiterated homogenization problem for the p-Laplacian equation in corrugated thin domains. Journal of Differential Equations, v. 392, p. 44-pg., 2024-02-22. (23/03847-6, 22/08112-1, 20/14075-6)

CARDONE, GIUSEPPE; FAELLA, LUISA; NAKASATO, JEAN CARLOS; PERUGIA, CARMEN. Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes. Annali di Matematica Pura ed Applicata, v. 203, n. 5, p. 36-pg., 2024-03-29. (23/03847-6, 22/08112-1)

NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries. ADVANCED NONLINEAR STUDIES, v. 23, n. 1, p. 38-pg., 2023-08-29. (22/08112-1, 20/14075-6, 20/04813-0)

LAURAIN, ANTOINE; LOPES, PEDRO T. P.; NAKASATO, JEAN C.. An abstract Lagrangian framework for computing shape derivatives. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, v. 29, p. 35-pg., 2023-01-11. (22/08112-1, 19/15200-1)