Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients

By Grégoire Nadin, Luca Rossi. 2015

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This paper is devoted to existence and non-existence results for generalized transition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coecients of the equation are periodic in space but otherwise depend in a fairly general fashion on time, we prove that such waves exist as soon as their speed is suciently large in a sense. When this speed is too small, transition waves do not exist anymore, this result holds without assuming periodicity in space. These necessary and sucient conditions are proved to be optimal when the coecients are periodic both in space and time. Our method is quite robust and extends to general non-periodic space-time heterogeneous coecients, showing that transition waves solutions of the nonlinear equation exist as soon as one can construct appropriate solutions of a given linearized equation.

Subfields: Mathematical Physics, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/2aa7a4ca74832021a011a89ddbdfb03831e14fb6