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Traveling wave solutions with mixed dispersal for spatially periodic Fisher-KPP equations. (English) Zbl 1310.35064
Summary: Traveling wave solutions to a spatially periodic nonlocal/random mixed dispersal equation with KPP nonlinearity are studied. By constructions of super/sub solutions and comparison principle, we establish the existence of traveling wave solutions with all propagating speeds greater than or equal to the spreading speed in every direction. For speeds greater than the spreading speed, we further investigate their uniqueness and stability.

MSC:
35C07 Traveling wave solutions
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
45C05 Eigenvalue problems for integral equations
45G10 Other nonlinear integral equations
92D25 Population dynamics (general)
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