A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system

This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain () with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data. We will consi...

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Published in:Nonlinearity 2018-04, Vol.31 (4), p.1639-1672
Main Authors: Fujie, Kentarou, Senba, Takasi
Format: Article
Language:English
Subjects:
chemotaxis
sensitivity function
time-global existence
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description This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain () with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function χ for the global existence of solutions under the assumption of smallness of the constant τ.
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subjects chemotaxis
sensitivity function
time-global existence
title A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
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