EVOLUTION MODELS ON QUANTUM METRIC GRAPHS

• Grant number: 25/25039-4
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2026
• End date: October 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jaime Angulo Pava
• Grantee: Jaime Angulo Pava
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• City of the host institution: São Paulo

Abstract

In recent years, there has been significant and growing interest among researchers from various fields-including experimentalists, pure and applied mathematicians, engineers, and physicists-in the modeling and analysis of evolutionary problems described by partial differential equations (PDEs) on graphs or branched systems. In this context, PDEs on branched networks emerge as a fertile field for investigating soliton propagation and nonlinear dynamics, which are fundamental for describing highly complex physical phenomena such as Bose-Einstein condensates in networks, superconductor networks, neuroscience, DNA, blood pressure waves in long arteries, etc.Despite this potential, there remains a lack of analytical studies dedicated to understanding the dynamics induced in graphs by most of the highly relevant nonlinear models in this field, such as the dispersive Schrodinger and Korteweg-de Vries models, or the diffusion Nagumo models. For example, the study of the mechanism that induces stable or unstable behavior in the propagation of structures such as solitons in networks remains unclear because it is not possible to clearly see how energy travels through the network. Therefore, one of the objectives of this project is to develop new analytical tools that allow us to describe and predict the dynamics of these evolutionary models. We emphasize that the study of evolution equations in metric graphs is a growing area in Brazil, and the proponent is one of the most active researchers in this field. (AU)