Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones. (English) Zbl 0767.45005

Holmåker, Kjell

SIAM J. Math. Anal. 24, No. 1, 116-128 (1993).

The 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	Asymptotics of solutions to integral equations
45M10	Stability theory for integral equations
92C45	Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
45F05	Systems of nonsingular linear integral equations

Keywords:

global asymptotic stability; self-organization of cellular patterns; liver zones; system of integro-differential equations; stationary solution; jump discontinuity