Asymptotic analysis in differential and integral equations

• Grant number: 17/02630-2
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2017
• End date: July 31, 2019
• 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

Our aim here is analyze integral and partial differential equations under singular perturbations. We consider boundary value problems with parameters driven by applied areas studying their behavior in order to extract limit problems and convergence. The main parameters that we deal with here are (i) the domain of the solutions (boundary perturbation problems), (ii) nonlinear terms in the equations (nonlinear analysis), and (iii) the coefficients of the problems. (AU)

Scientific publications

(10)

(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)

NOGUEIRA, ARIADNE; NAKASATO, JEAN CARLOS; PEREIRA, MARCONE CORREA. Concentrated reaction terms on the boundary of rough domains for a quasilinear equation. Applied Mathematics Letters, v. 102, APR 2020. (17/02630-2)

PEREIRA, MARCONE C.. Nonlocal evolution equations in perforated domains. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 41, n. 16, p. 6368-6377, NOV 15 2018. (17/02630-2)

LOPES, PEDRO T. P.; PEREIRA, MARCONE C.. Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation. Journal of Mathematical Analysis and Applications, v. 465, n. 1, p. 379-402, SEP 1 2018. (16/07016-8, 17/02630-2)

ARRIETA, JOSE M.; NOGUEIRA, ARIADNE; PEREIRA, MARCONE C.. NONLINEAR ELLIPTIC EQUATIONS WITH CONCENTRATING REACTION TERMS AT AN OSCILLATORY BOUNDARY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 24, n. 8, SI, p. 4217-4246, AUG 2019. (17/02630-2)

NAKASATO, JEAN CARLOS; PAZANIN, IGOR; PEREIRA, MARCONE CORREA. Roughness-induced effects on the convection-diffusion-reaction problem in a thin domain. APPLICABLE ANALYSIS, v. 100, n. 5, JUN 2019. (17/02630-2)

PEREIRA, MARCONE C.; SASTRE-GOMEZ, SILVIA. Nonlocal and nonlinear evolution equations in perforated domains. Journal of Mathematical Analysis and Applications, v. 495, n. 2, MAR 15 2021. (17/02630-2)

PEREIRA, MARCONE; OLIVA, SERGIO; SARTORI, LARISSA. Time-scale analysis nonlocal diffusion systems, applied to disease models. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 43, n. 15, MAY 2020. (19/06221-5, 17/02630-2)

ARRIETA, JOSE M.; NOGUEIRA, ARIADNE; PEREIRA, MARCONE C.. Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v. 77, n. 2, p. 536-554, JAN 15 2019. (17/02630-2)

PEREIRA, MARCONE C.; ROSSI, JULIO D.. Nonlocal problems in perforated domains. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 150, n. 1, p. 305-340, FEB 2020. (15/17702-3, 17/02630-2)

ARRIETA, JOSE M.; NOGUEIRA, ARIADNE; PEREIRA, MARCONE C.. NONLINEAR ELLIPTIC EQUATIONS WITH CONCENTRATING REACTION TERMS AT AN OSCILLATORY BOUNDARY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 24, n. 8, p. 30-pg., 2019-08-01. (17/02630-2)