Methods and Applications of Analysis
Volume 18 (2011)
Positive stationary solutions and spreading speeds of KPP equations in locally spatially in homogeneous media
Pages: 427 – 456
The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations with local (i.e. the standard Laplacian) 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.
KPP equations, random dispersal, nonlocal dispersal, discrete dispersal, localized spatial inhomogeneity, spreading speed, positive stationary solution, principal eigenvalue, subsolution, super-solution, comparison principle
2010 Mathematics Subject Classification
35K57, 45G10, 58D20, 92D25