A hyperbolic Keller-Segel repulsion model proves existence, uniqueness and segregation for two cell populations and numerically finds competitive exclusion plus initial-total-number dependence of population ratios.
Asymptotic behavior of a nonlocal advection system with two populations
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abstract
In this paper, we consider a nonlocal advection model for two populations on a bounded domain. The first part of the paper is devoted to the existence and uniqueness of solutions and the associated semi-flow properties. Here we use the notion of solution integrated along the characteristics. Next, by proving segregation property, we construct an energy functional to investigate the asymptotic behavior of the solution. In order to get some compactness of the positive orbit, we use the narrow convergence in the space of Young measures. By using this idea, we get a description of the asymptotic behavior of the solution in the space of Young measures. The last section of the paper is devoted to numerical simulations, which confirm and complement our theoretical results.
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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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A cell-cell repulsion model on a hyperbolic Keller-Segel equation
A hyperbolic Keller-Segel repulsion model proves existence, uniqueness and segregation for two cell populations and numerically finds competitive exclusion plus initial-total-number dependence of population ratios.