Mathematical Analysis of Models of Chemotaxis with Biological Reactions

• Grant number: 24/17350-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2025
• End date: April 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gabriela Del Valle Planas
• Grantee: Crystianne Lilian de Andrade
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project aims to promote theoretical advances in the field of partial differential equations, focusing on equations that model chemotaxis in anomalous diffusion dynamics, coupled with other phenomena, such as biological reactions in fluid environments. The research will analyze Keller-Segel systems and their generalizations, incorporating the fractional Laplacian to model superdiffusion. The goal is to establish well-posedness results, both local and global, and regularity estimates for mild solutions in Sobolev spaces. The relevance of this project lies in understanding how different diffusion regimes affect the dynamics of chemotaxis and biological reactions in fluid environments, directly influencing the solutions to the problems analyzed.