Stability analysis of stationary waves for reaction diffusion-degenerate equations on a Y-junction graph.

• Grant number: 24/15816-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: November 02, 2024 - November 15, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jaime Angulo Pava
• Grantee: Jaime Angulo Pava
• Visiting researcher: Ramon Gabriel Plaza Villegas
• Visiting researcher institution: Universidad Nacional Autónoma de México (UNAM), Mexico
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we intend to study the dynamics of Nagumo-type models (which extend the classical Fisher-KPP equation) on Y-junction metric graphs. This evolution model appears in applications from phase transitions in crystallography to biological models with degenerate cell motility. The focus of our proposal will be to continuing our study on the existence of stationary states and their stability properties (spectral and/or nonlinear). Our research project can be classified as innovative and in recent years the proponent and the collaborating professor Prof. Ramon Plaza (UNAM-Mexico) have obtained relevant results for other evolutionary models on metric graphs. (AU)