Global existence of solutions to an attraction-repulsion chemotaxis model with growth

Sainan Wu; Junping Shi; Boying Wu

doi:10.3934/cpaa.2017050

Article Contents

2017, Volume 16, Issue 3: 1037-1058. Doi: 10.3934/cpaa.2017050

This issue Previous Article Boundary layer analysis from the Keller-Segel system to the aggregation system in one space dimension Next Article Stabilizing blow up solutions to nonlinear schrÖdinger equations

Global existence of solutions to an attraction-repulsion chemotaxis model with growth

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China
2.
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA

Received: May 31, 2016

Revised: October 31, 2016

Published: January 2018

S. Wu is supported in part by a grant from China Scholarship Council; J. Shi is partially supported by US-NSF grant DMS-1313243 and B. Wu is partially supported by National Natural Science Foundation of China grant No. 11271100.

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Abstract

An attraction-repulsion chemotaxis model with nonlinear chemotactic sensitivity functions and growth source is considered. The global-in-time existence and boundedness of solutions are proved under some conditions on the nonlinear sensitivity functions and growth source function. Our results improve the earlier ones for the linear sensitivity functions.

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Mathematics Subject Classification: 35K57, 35K59; 35B45, 92C17.

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Figure 1. Regions in (p, q) plane where the global existence and boundedness of solutions to (1.9) are proved. The regions labelled by (ⅰ), (ⅱ), (ⅲ) and (iv) correspond to the ones defined in Theorems 1.1 and 1.2, and for the region labelled with?, the result is not known. Left: n ≤ 2; Right: n > 2

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