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On the uniqueness and stability of positive solutions in the Lotka- Volterra competition model with diffusion. (English) Zbl 0721.92025
Consider the Lotka-Volterra system \[ u_ t=\Delta u+u[a-bu-cv],\quad v_ t=\Delta v+v[d-eu-fv] \] in a cylinder \(\Omega\times (0,\infty)\), where \(\Omega\) is an open, bounded smooth domain in \({\mathbb{R}}^ N\) together with homogeneous Dirichlet boundary conditions on \(\partial \Omega \times (0,\infty)\). All coefficient functions are assumed to be nonnegative and constant. The authors study the question of uniqueness and stability of componentwise positive steady state solutions to the above-mentioned system in the case of unequal growth rates (a,d).
Reviewer: R.Manthey (Jena)

92D40 Ecology
35K20 Initial-boundary value problems for second-order parabolic equations
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)