Numerical study of two-species chemotaxis models

Alexander Kurganov; Mária Lukáčová-Medvidová

doi:10.3934/dcdsb.2014.19.131

Article Contents

2014, Volume 19, Issue 1: 131-152. Doi: 10.3934/dcdsb.2014.19.131

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Numerical study of two-species chemotaxis models

Alexander Kurganov^1, and
Mária Lukáčová-Medvidová^2,

1.
Mathematics Department, Tulane University, 6823 St. Charles Ave, New Orleans, LA 70118
2.
Institute of Mathematics, University of Mainz, Staudingerweg 9, 55099 Mainz

Received: November 30, 2011

Revised: June 30, 2013

Published: December 2013

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Abstract

We first conduct a comparative numerical study of two recently proposed two-species chemotaxis models. We show that different scenarios are possible: depending on the initial masses, either one or both cell densities may blow up, or a global solution may exist. In particular, our numerical results indicate answers on some open questions of possible blow up stated in [4,7]. We then introduce two regularizations of the studied models and demonstrate that their solutions are capable of developing spiky structure without blowing up.

Keywords:

Two-species chemotaxis models,
second-order positivity preserving finite-volume method,
finite-time blow-up.

Mathematics Subject Classification: Primary: 92C17, 76M12; Secondary: 65M06, 35K55, 35B40.

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