Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model

Abstract

Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= Δn - \nabla \cdot (n \nabla c), \\ 0 &= Δc - nc, \end{align*} under no-flux boundary conditions for $n$ and Robin-type boundary conditions \[ \partial_ν c = (γ-c) g \] for $c$ (with $\gamma >0$ and $C^{1+\beta }(\partial \Omega )\ni g>0$ for some $\beta \in (0,1)$) are established in bounded domains $\Omega \subset {\mathbb{R}}^N$, $N\ge 1$. Under a smallness condition on $\gamma$, moreover, we show convergence to the stationary solution.

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Cited by in corpus (4)

• Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary
• Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation
• Transition layers to chemotaxis-consumption models with volume-filling effect
• Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption