Traveling wave solutions with mixed dispersal for spatially periodic Fisher-KPP equations

Pages: 815 - 824, Issue special, November 2013

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Aijun Zhang - Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States (email)

Abstract: 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.

Keywords:  Fisher-KPP equation, random dispersal, nonlocal dispersal, principal eigenvalue, spreading speed.
Mathematics Subject Classification:  Primary: 34L15, 35K55, 35K57, 37L60, 45C05, 45G10, 45M20; Secondary: 92D25.

Received: September 2012;      Revised: December 2012;      Published: November 2013.