Global existence for a chemotaxis-haptotaxis model with $ p $-Laplacian

Changchun Liu; Pingping Li

doi:10.3934/cpaa.2020070

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2020, Volume 19, Issue 3: 1399-1419. Doi: 10.3934/cpaa.2020070

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Global existence for a chemotaxis-haptotaxis model with $ p $-Laplacian

Changchun Liu and
Pingping Li

Department of Mathematics, Jilin University, Changchun 130012, China

Received: April 2019

Revised: September 2019

Published: March 2020

This work is supported by the Jilin Scientific and Technological Development Program (no. 20170101143JC)

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Abstract

This paper deals with a chemotaxis-haptotaxis model with the slow $ p $-Laplacian diffusion in three-dimensional smooth bounded domains. It is proved that for any $ p>2 $, the chemotaxis-haptotaxis model problem admits a global bounded weak solution if $ \frac{\chi}{\mu} $ is appropriately small.

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Mathematics Subject Classification: Primary: 92C17, 35K51; Secondary: 35K65, 35K92.

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