# American Institute of Mathematical Sciences

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Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
February  2020, 13(2): 257-268. doi: 10.3934/dcdss.2020014

## 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

Received  May 2017 Revised  May 2018 Published  January 2019

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.

Citation: Monica Marras, Stella Vernier-Piro, Giuseppe Viglialoro. Decay in chemotaxis systems with a logistic term. Discrete & Continuous Dynamical Systems - S, 2020, 13 (2) : 257-268. doi: 10.3934/dcdss.2020014
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