Global existence theorem for a model governing the motion of two cell populations

Brock C. Price; Xiangsheng Xu

doi:10.3934/krm.2020042

Article Contents

2020, Volume 13, Issue 6: 1175-1191. Doi: 10.3934/krm.2020042

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Global existence theorem for a model governing the motion of two cell populations

Brock C. Price and
Xiangsheng Xu

Department of Mathematics & Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Received: March 31, 2020

Revised: June 30, 2020

Early access: September 2020

Published: November 2020

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Abstract

This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the coefficient matrix is non-symmetric and degenerate in the sense that its determinant is $ 0 $. The existence assertion is established by exploring the fact that the total population density satisfies a porous media equation.

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Mathematics Subject Classification: Primary: 35B45, 35K57, 35K55, 35K65, 35Q92; Secondary: 76N10.

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References

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