We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated. The second part is devoted to singular limit problems for solutions of the PDE system and traveling wave solutions, respectively. Actually, the contact inhibition model considered in this paper possesses quite similar properties to those of the Fisher-KPP equation. In particular, the limit problems reveal a relation between the contact inhibition model and the Fisher-KPP equation.

Bertsch, M., Hilhorst, D., Izuhara, H., Mimura, M., Wakasa, T. (2020). A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher KPP equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 40(6), 3117-3142 [10.3934/dcds.2019226].

A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher KPP equation

Bertsch M.;
2020-01-01

Abstract

We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated. The second part is devoted to singular limit problems for solutions of the PDE system and traveling wave solutions, respectively. Actually, the contact inhibition model considered in this paper possesses quite similar properties to those of the Fisher-KPP equation. In particular, the limit problems reveal a relation between the contact inhibition model and the Fisher-KPP equation.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Parabolic-hyperbolic system; degenerate Fisher-KPP equation; segregation property; singular limit; traveling wave solution
Bertsch, M., Hilhorst, D., Izuhara, H., Mimura, M., Wakasa, T. (2020). A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher KPP equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 40(6), 3117-3142 [10.3934/dcds.2019226].
Bertsch, M; Hilhorst, D; Izuhara, H; Mimura, M; Wakasa, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/244288
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