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 special type. In this paper it is proved that this stationary solution is in fact globally asymptotically stable, that is, it is the limit (as time tends to infinity) of the solution of the integro-differential equations for arbitrary initial values.
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Kjell Holmåker (1993) studied this question.