Asymptotic and qualitative analysis of partial differential equations

• Grant number: 23/01225-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2023
• End date: December 19, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcone Corrêa Pereira
• Grantee: Estefani Moraes Moreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In what follows, we present a proposal of an activity plan idealized for the developmentof the postdoctoral research activities of Estefani Moraes Moreira, under the supervision ofMarcone C. Pereira, professor of Departamento de Matem´atica Aplicada (MAP), of Institutode Matemática e Estatística (IME) of Universidade de São Paulo (USP).This proposal addresses mostly questions related to asymptotic and qualitative analysisin boundary value problems, whose interest comes from modeling phenomena via PartialDifferential Equations. In a general matter, the phenomena of our interest suggest theintroduction of parameters in the equation with specific behaviors that are associated withthe performance of the model, transfering to them a huge importance in the model process.There are three most important parameters we intend to approach in this context: (i)the domain of definition of solutions of differential/integral equations; (ii) non-linear terms that perturbate the equations; (iii) the coefficients of the boundary value problems.

Scientific publications

(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.; CARVALHO, ALEXANDRE N.; MOREIRA, ESTEFANI M.; VALERO, JOSE. BIFURCATION AND HYPERBOLICITY FOR A NONLOCAL QUASILINEAR PARABOLIC PROBLEM. Advances in Differential Equations, v. 29, n. 1-2, p. 26-pg., 2024-01-01. (23/01225-8, 18/00065-9, 20/00104-4, 20/14075-6)

MOREIRA, ESTEFANI M.; VALERO, JOSE. The Existence of Isolating Blocks for Multivalued Semiflows. Journal of Dynamics and Differential Equations, v. 36, n. 4, p. 32-pg., 2024-01-19. (23/01225-8, 18/00065-9, 20/00104-4)

MOREIRA, ESTEFANI M.; VALERO, JOSE. THE INDEX THEORY FOR MULTIVALUED DYNAMICAL SYSTEMS WITH APPLICATIONS TO REACTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS NONLINEARITY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, v. 17, n. 3, p. 19-pg., 2023-11-23. (23/01225-8, 18/00065-9, 20/00104-4)