Special Session 1: Analysis of parabolic models for chemotaxis

Some discussions regarding the seminal Keller-Segel model with positive total flux
Giuseppe Viglialoro
Universit \\`a degli Studi di Cagliari
Italy
Co-Author(s):    Silvia Frassu, Yuya Tanaka
Abstract:
Since the advent of the seminal Keller-Segel models describing chemotaxis phenomena involving some cell and chemical distributions, the results obtained for related variants are innumerable. Nevertheless, the common denominator of such studies focuses on the assumption that the equation for the cells obeys a zero-flux boundary condition (impenetrable domains). The aim of this talk is to discuss preliminary results and share considerations on chemotaxis models where the total flux has a positive sign (penetrable domains). This is a joint project with Silvia Frassu and Yuya Tanaka.