Sharp profiles for diffusive logistic equation with spatial heterogeneity

Abstract

In this article, we study the sharp profiles of positive solutions to the diffusive logistic equation. By employing parameters and analyzing the corresponding perturbation equations, we find the effects of boundary and spatial heterogeneity on the positive solutions. The main results exhibit the sharp effects between boundary conditions and linear/nonlinear spatial heterogeneities on positive solutions.

Keywords

• reaction–diffusion
• logistic equation
• heterogeneity
• positive solution
• 35b40
• 35k57
• 92d25