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

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