Asymptotic and qualitative analysis of integro-differential equations

• Grant number: 20/04813-0
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2020
• End date: July 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcone Corrêa Pereira
• Grantee: Marcone Corrêa Pereira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In the following we present a descriptive activity plan of proposals idealized for the accomplishment of the research activities of Marcone C. Pereira, professor of the Department of Applied Mathematics (MAP) of the Institute of Mathematics and Statistics (IME) of the University of São Paulo (USP).We will see that the proposal developed mainly addresses qualitative issues associated with the theme Asymptotic Analysis of Contour Value Problems, whose interest is remote to phenomena modeled by Partial Differential Equations (EDPs) and Integral Equations. In general, the phenomena of our interest suggest the introduction of parameters in the equation with specific behaviors that are associated with model performance, transferring great importance to them in the modeling process.Three are the most important parameters that we intend to address in this context: (i) the domain for defining EDP solutions; (ii) nonlinear terms that disturb the equation; (iii) the coefficients of the proposed boundary value problems. (AU)

Scientific publications

(8)

(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)

ARRIETA, JOSE M.; CARLOS NAKASATO, JEAN; CORREA PEREIRA, MARCONE. The p-Laplacian equation in thin domains: The unfolding approach. Journal of Differential Equations, v. 274, p. 1-34, FEB 15 2021. (20/04813-0)

CAPANNA, MONIA; NAKASATO, JEAN C.; PEREIRA, MARCONE C.; ROSSI, JULIO D.. HOMOGENIZATION FOR NONLOCAL PROBLEMS WITH SMOOTH KERNELS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 41, n. 6, p. 2777-2808, JUN 2021. (20/04813-0)

BENGURIA, RAFAEL D.; PEREIRA, MARCONE C.; SAEZ, MARIEL. The Hadamard formula for nonlocal eigenvalue problems. MATHEMATISCHE ANNALEN, v. N/A, p. 29-pg., 2023-07-18. (20/14075-6, 20/04813-0)

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. 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)

NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. The p-Laplacian in thin channels with locally periodic roughness and different scales. Nonlinearity, v. 35, n. 5, p. 39-pg., 2022-05-05. (20/14075-6, 20/04813-0)

NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. n optimal control problem in a tubular thin domain with rough boundar. Journal of Differential Equations, v. 313, p. 188-243, MAR 15 2022. (20/14075-6, 20/04813-0)

NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. A CLASSICAL APPROACH FOR THE p-LAPLACIAN IN OSCILLATING THIN DOMAINS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 58, n. 1, p. 209-231, SEP 2021. (20/04813-0)