Asymptotic behavior of global solutions of aerotaxis equations

Abstract We study asymptotic behavior of global solutions of one-dimensional aerotaxis model proposed in Knosalla and Nadzieja (2015) [9] .

Stationary solutions of aerotaxis equations

Steady‐state solutions of the aerotaxis problem

We study the steady-state system of aerotaxis equations in higher dimensions.It is shown that the existence and multiplicity of solutions depend on the totalmass of the colony of bacteria, the energy function, and the boundary conditions.

On the steady state problem of the chemotaxis-consumption model with logistic growth and Dirichlet boundary condition for signal

This paper concerns the steady state problem for chemotaxis consumption system with logistic growth and constant concentration of chemoat-tractant on the boundary of the domain. We establish the existence of a non-constant positive solution to this problem. The uniqueness of this solution is obtained under the smallness assumption on the boundary data. Some qualitative properties of the solutions and numerical results are presented.

Global solutions of aerotaxis equations

We study the existence of the global solutions in a model de- scribing the evolution of density of bacteria and oxygen dissolved in water lling a capillary. In the proof of local existence of classical solutions we use Amann theory. The Moser{Alikakos technique is the main tool for the proof of L1 boundedness of local solutions.