This paper deals with a parabolic-parabolic Keller-Segel type system in a three dimensional spatial domain. The problem is characterized by time dependent coeficients and source and damping terms. The existence of non-negative and blowing-up solutions at a finite time t* is assumed and, subsequently, explicit lower bounds for such a t* are derived under suitable conditions on the coeficients, the source and damping terms and the spatial domain.
Blow-up time of a general Keller-Segel system with source and damping terms
MARRAS, MONICA;VIGLIALORO, GIUSEPPE
2016
Abstract
This paper deals with a parabolic-parabolic Keller-Segel type system in a three dimensional spatial domain. The problem is characterized by time dependent coeficients and source and damping terms. The existence of non-negative and blowing-up solutions at a finite time t* is assumed and, subsequently, explicit lower bounds for such a t* are derived under suitable conditions on the coeficients, the source and damping terms and the spatial domain.
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