Decay in chemotaxis systems with a logistic term

Monica Marras; Stella Vernier-Piro; Giuseppe Viglialoro

doi:10.3934/dcdss.2020014

Article Contents

2020, Volume 13, Issue 2: 257-268. Doi: 10.3934/dcdss.2020014

This issue Previous Article Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system Next Article Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity

Decay in chemotaxis systems with a logistic term

Università di Cagliari, Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy

* Corresponding author: Monica Marras
* Corresponding author: Monica Marras

Received: April 30, 2017

Revised: April 30, 2018

Published: February 2020

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Abstract

This paper is concerned with a general fully parabolic Keller-Segel system, defined in a convex bounded and smooth domain $Ω$ of $\mathbb{R}^N, $ for N∈{2, 3}, with coefficients depending on the chemical concentration, perturbed by a logistic source and endowed with homogeneous Neumann boundary conditions. For each space dimension, once a suitable energy function in terms of the solution is defined, we impose proper assumptions on the data and an exponential decay of such energies is established.

Keywords:

Nonlinear parabolic systems,
asymptotic behavior,
chemotaxis,
PDEs in connection with biology and other natural sciences.

Mathematics Subject Classification: Primary: 35K55, 35B40; Secondary: 92C17, 35Q92.

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References

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