TESdE: Thematic on Equations and Systems of differential Equations

• Grant number: 22/16407-1
• Support Opportunities: Research Projects - Thematic Grants
• Duration: October 01, 2023 - September 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ederson Moreira dos Santos
• Grantee: Ederson Moreira dos Santos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Pesquisadores principais: Olimpio Hiroshi Miyagaki
• Associated researchers: Adilson Eduardo Presoto ; Djairo Guedes de Figueiredo ; Eugenio Tommaso Massa ; Francisco Odair Vieira de Paiva ; Gaetano Siciliano ; Gustavo Ferron Madeira ; Marcos Tadeu de Oliveira Pimenta ; Sergio Henrique Monari Soares ; Sérgio Leandro Nascimento Neves ; Vanderley Alves Ferreira Junior
• Associated grant(s): 23/14636-6 - Gradient estimates and hopf-Oleinik lemma for quasilinear non-uniformly elliptic operators and applications, AV.BR
• Associated scholarship(s): 24/05733-0 - Semilinear equations with absorption nonlinearities and measures as data, BP.MS; 24/15858-5 - Initiation to Variational Inequalities, BP.IC; 24/14947-4 - Introduction to variational methods, BP.IC; + associated scholarships 24/02878-8 - Non-standard analysis, Ultrafunçtions, infinites and infinitesimals, with applications, BP.IC; 24/02669-0 - Study of mean curvature problems by elliptic regularization, BP.MS; 24/04864-4 - Analytic functions and the fluid dynamics, BP.IC; 24/03431-7 - Shape optimization and Brouwer topological degree, BP.IC - associated scholarships

Abstract

This project is dedicated to the study of problems involving partial differential equations (PDEs) of elliptic and evolution type, which may include non-local terms. It points questions about the existence and multiplicity and also about qualitative properties, such as symmetry, bifurcation, decay, energy, unique continuation principles, concentration, blow up, and stability of solutions to problems involving second and fourth orders PDEs, as well as second-order systems of PDEs. This project also intersects the areas of functional analysis, differential geometry, ordinary differential equations (ODEs) and numerical simulations for the study of ODEs and PDEs. (AU)