One-dimensional chemotaxis kinetic model

The one-dimensional chemotaxis model: global existence and asymptotic profile

Osaki and Yagi (2001) give a proof of global existence for the classical chemotaxis model in one space dimension with use of energy estimates. Here we present an alternative proof which uses the regularity properties of the heat-equation semigroup. With this method we can identify a large selection of admissible spaces, such that the chemotaxis model de nes a global semigroup on these spaces. W...

One-dimensional kinetic Ising model with nonuniform coupling constants

A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown that there are cases where the system exhibits a static phase transition, which is a change of behavior of the static profile of the expectation values of th...

On Electro-kinetic Fluids: One Dimensional Configurations

Electro-kinetic fluids can be modeled by hydrodynamic systems describing the coupling between fluids and electric charges. The system consists of a momentum equation together with transport equations of charges. In the dynamics, the special coupling between the Lorentz force in the velocity equation and the material transport in the charge equation gives an energy dissipation law. In stationary...

Stationary solutions with vacuum for a one-dimensional chemotaxis model with non-linear pressure

In this article, we study a one-dimensional hyperbolic quasilinear model of chemotaxis with a non-linear pressure and we consider its stationary solutions, in particular with vacuum regions. We study both cases of the system set on the whole line R and on a bounded interval with no-flux boundary conditions. In the case of the whole line R, we find only one stationary solution, up to a translati...

Numerical simulation of a kinetic model for chemotaxis