# American Institute of Mathematical Sciences

2015, 2015(special): 409-417. doi: 10.3934/proc.2015.0409

## On explicit lower bounds and blow-up times in a model of chemotaxis

 1 Department of Mathematics and Computer Science, University of Cagliari, V. Ospedale 72, 09124. Cagliari, Italy 2 Department of Mathematics and Computer Science, University of Cagliari, V. le Merello 92, 09123. Cagliari, Italy, Italy

Received  September 2014 Revised  October 2014 Published  November 2015

This paper is concerned with a parabolic Keller-Segel system in $\mathbb{R}^n$, with $n=2$ or $3$, under Neumann boundary conditions. First, important theoretical and general results dealing with lower bounds for blow-up time estimates are summarized and analyzed. Next, a resolution method is proposed and used to both compute the real blow-up times of such unbounded solutions and analyze and discuss some of their properties.
Citation: Maria Antonietta Farina, Monica Marras, Giuseppe Viglialoro. On explicit lower bounds and blow-up times in a model of chemotaxis. Conference Publications, 2015, 2015 (special) : 409-417. doi: 10.3934/proc.2015.0409
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