Lower bounds for blow-up in a parabolic-parabolic Keller-Segel system

Monica  Marras; Stella Vernier  Piro; Giuseppe  Viglialoro

doi:10.3934/proc.2015.0809

Article Contents

2015, Volume 2015: 809-816. Doi: 10.3934/proc.2015.0809 open access

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Lower bounds for blow-up in a parabolic-parabolic Keller-Segel system

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

Received: August 31, 2014

Revised: January 31, 2015

Published: October 2015

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Abstract

This paper deals with a parabolic-parabolic Keller-Segel system, modeling chemotaxis, with time dependent coefficients. We consider non-negative solutions of the system which blow up in finite time $t^*$ and an explicit lower bound for $t^*$ is derived under sufficient conditions on the coefficients and the spatial domain.

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Mathematics Subject Classification: Primary: 35K55, 35B44. Secondary: 92C17.

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References

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