Special Session 56: Variational methods for nonlinear PDEs

On some properties of unbounded solutions to a class of chemotaxis models

Alessandro Columbu
Universit\`a di Cagliari
Italy
Co-Author(s):    Silvia Frassu, Giuseppe Viglialoro
Abstract:
In this talk we consider an attraction-repulsion chemotaxis model with logistic, and with nonlinear rates for diffusion, sensitivities and productions of both chemoattractant and chemorepellent. We detect Lebesgue spaces where solutions blow-up and, additionally, we estimate the blow-up time. Finally, we establish some blow-up criteria in a simplified case of the model. This is a joint work with Silvia Frassu and Giuseppe Viglialoro.