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Volume 18,     Number 4,     Winter 2010

 

POPULATION DYNAMICS IN RIVERS:
ANALYSIS OF STEADY STATES
OLGA VASILYEVA AND FRITHJOF LUTSCHER

Abstract. We study a diffusion-reaction-advection equation describing population dynamics of aquatic organisms subject to a constant downstream drift in a bounded or semi-infinite domain. We analyze the nontrivial steady state solutions satisfying reflecting upstream and out flow downstream boundary conditions (Danckwerts' boundary conditions). We determine the behavior of the domain size as a function of the upstream/downstream density, show stability of the steady state, and investigate how certain qualitative aspects of the steady-state solution depend on advection speed.

 

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