The degenerate logistic model and a singularly mixed boundary blow-up problem

Abstract

We study the degenerate logistic model described by the equation ut-Δu=au-b(x)u^p with standard boundary conditions, where p>1, b vanishes on a nontrivial subset Ω₀ of the underlying bounded domain Ω⊂ℝ^N and b is positive on Ω₊... We consider the difficult case where ∂Ω₀⋂∂Ω≠... and ∂Ω₊⋂∂Ω≠... and examine the asymptotic behaviour of the solutions. By a detailed study of a singularly mixed boundary blow-up problem, we obtain some basic results on the dynamics of the model.