Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones.

*(English)*Zbl 0767.45005The formation of liver zones is modeled by a system of integro- differential equations. It has previously been proved that one particular stationary solution, characterized by a jump discontinuity at the zone boundary, is asymptotically stable with respect to sufficiently small perturbations of a certain type.

In this paper the author proves that this stationary solution is in fact globally asymptotically stable.

Reviewer: S.Anita (Iaşi)

##### MSC:

45K05 | Integro-partial differential equations |

45M05 | Asymptotic theory of integral equations |

45M10 | Stability theory of integral equations |

92C45 | Kinetics in biochemical problems |

45F05 | Systems of nonsingular linear integral equations |