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Zbl 0767.45005
Holmåker, Kjell
Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones. (English)
[J] SIAM J. Math. Anal. 24, No.1, 116-128 (1993). ISSN 0036-1410; ISSN 1095-7154/e

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.\par In this paper the author proves that this stationary solution is in fact globally asymptotically stable.
[S.Anita (Iaşi)]

MSC 2000:: *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

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

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