Special Session 1: Analysis of parabolic models for chemotaxis

Boundedness in a class of Keller--Segel models with dissipative gradient terms
Alessandro Columbu
Universit\`a degli Studi di Cagliari
Italy
Co-Author(s):    Tongxing Li; Daniel Acosta Soba; Giuseppe Viglialoro;
Abstract:
We study a class of zero-flux attraction-repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density, the chemosensitivities and the production rates of the chemoattractant and the chemorepellent. Additionally, a source involving also the gradient of the biological distribution is incorporated. In this talk we will see a sketch of the proof for the existence of solutions and we will find a condition for the boundedness.