Positive Stationary Solutions and Spreading Speeds of KPP Equations in Locally Spatially Inhomogeneous Media

Abstract

The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations with random or nonlocal or discrete dispersal in locally spatially inhomogeneous media. It is shown that such an equation has a unique globally stable positive stationary solution and has a spreading speed in every direction. Moreover, it is shown that the localized spatial inhomogeneity of the medium neither slows down nor speeds up the spatial spreading in all the directions.

References in corpus (3)

• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
• Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations

Cited by in corpus (2)

• On Bounded Positive Stationary Solutions for a Nonlocal Fisher-KPP Equation
• Effects of localized spatial variations on the uniform persistence and spreading speeds of time periodic two species competition systems