Abstract
The current paper investigate the persistence of positive solutions of KPP type evolution equations with random/nonlocal dispersal in locally spatially inhomogeneous habitat. By the constructions of super/sub solutions and comparison principle, we prove that such an equation has a unique globally stable positive stationary solution.
Highlights
The current paper investigate the persistence of positive solutions of KPP type evolution equations with random/nonlocal dispersal in locally spatially inhomogeneous habitat
By the constructions of super/sub solutions and comparison principle, we prove that such an equation has a unique globally stable positive stationary solution
We consider (1.1) in the case that the growth rates depend on the space variable, but only when it is in some bounded subset of the underlying habitat, which reflects the localized spatial inhomogeneity of the media
Summary
The current paper is concerned with persistence of species in locally spatially variational environments or habitat, where (Au)(t, x). To model the population dynamics of such species in the case that the underlying environment is continuous, the nonlocal dispersal equation (1.3) is often used. This paper propose to study a mixed dispersal strategy, that is, a hybrid of random and non-local dispersal. Vol 9, No 1; 2017 single species and how the hybrid dispersal strategies will evolve in spatially locally inhomogeneous environment (see H1 and H2). We consider (1.1) in the case that the growth rates depend on the space variable, but only when it is in some bounded subset of the underlying habitat, which reflects the localized spatial inhomogeneity of the media. Equations (1.6) has a unique positive constant stationary solution u0.
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