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Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems
Journal article   Open access   Peer reviewed

Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems

Tong Li and Anthony Suen
Discrete and continuous dynamical systems, Vol.36(2), pp.861-875
08/2015
DOI: 10.3934/dcds.2016.36.861
url
https://doi.org/10.3934/dcds.2016.36.861View
Published (Version of record) Open Access

Abstract

We prove the global-in-time existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain of ℝ2 or ℝ3 with initial chemical concentration small in H1. No smallness assumption is imposed on the initial cell density which is in L2. We first show that when the initial chemical concentration c0 is small only in H1 and (n0-n∞; c0) is smooth, the classical solution exists for all time. Then we construct weak solutions as limits of smooth solutions corresponding to mollified initial data. Finally we determine the asymptotic behavior of the global solutions.

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