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Existence and uniqueness of the weak solution for Keller-Segel model coupled with Boussinesq equations

Slimani Ali, Bouzettouta Lamine, Guesmia Amar

Demonstratio Mathematica

2021

Vol. 54, nr 1

558--575

Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method.

Cells and attractant masses related by chemotactic aggregation

Domański Z.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

23-28

The active role played by chemotactic current density of the migrating cells in order to overcome its diffusion current, leads to a spatially - non-homogeneous and time - presistent distribution of the cells. We show that independently of the initial attractant concentration, its quantity tends exponentially to the concentration of cells as the system approaches a steady state.