Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption

By Johannes Lankeit, Yulan Wang. 2016

150 citations recorded by the source corpus.

This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array} \end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\mu$ and prove that for any $\mu>0$ there exists a weak solution. Moreover, in the case of $\kappa>0$ convergence to the constant equilibrium $(\frac{\kappa}{\mu},0)$ is shown.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/c5da745c0f1ee536f3b78e0738d94f069877b557

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Citations in the corpus

Analysis of a chemotaxis model with indirect signal absorption (2019, background): “In many cases, for instance in [10, 20, 21], the authors utilize the functional”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “2 ([65]) Let n ≥ 2 and Ω ⊂ R be a bounded domain with smooth boundary, and let f be as in (4.”