Qualitative Properties of Continuous and Impulsive Dynamical Systems: Asymptotic Dynamics and Oscillation Theory

• Grant number: 24/07880-0
• Support Opportunities: Scholarships abroad - Research
• Start date: January 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Everaldo de Mello Bonotto
• Grantee: Everaldo de Mello Bonotto
• Host Investigator: Tomas Caraballo Garrido
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Sevilla (US), Spain
• Associated research grant: 20/14075-6 - Dynamical systems and their attractors under perturbations, AP.TEM

Abstract

This scientific research project focuses on the theory of continuous dynamical systems, as well as the theory of dynamical systems whose evolution is interrupted by abrupt changes of state that can be considered instantaneous. The project is part of the qualitative study of continuous and impulsive dynamical systems. We aim to study the asymptotic dynamics of semilinear partial differential equations, both in the presence and absence of impulses. Additionally, we intend to establish the oscillation theory for impulsive evolution processes.