Abstract
In this paper, we consider a two-species predator-prey model in advective heterogeneous environments with the Holling-Tanner interaction term, where the Danckwerts boundary conditions are imposed. Existence, uniqueness, and multiplicity of positive steady state solutions are investigated by using the degree theory and super-sub solution method for predator-prey systems and analyzing the limiting profile. Using the comparison principle for parabolic equations, persistence theory, and constructing Lyapunov functions, we establish various results on the long-time dynamics.
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