Communications in Mathematical Sciences

Volume 12 (2014)

Number 5

Transition waves for a class of space-time dependent monostable equations

Pages: 879 – 900



Luca Rossi (Dipartimento di Matematica, Università di Padova, Italy)

Lenya Ryzhik (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)


We investigate the existence of generalized transition waves for reaction-diffusion KPP equations depending explicitly on time and space. In the case of spatially periodic diffusion and drift, and general temporal dependence of the nonlinearity, we almost completely characterize the set of admissible speeds of the waves in terms of a suitable notion of mean introduced in [15]. A lower bound for the speeds is also derived for equations with non-periodic, spatially dependent coefficients, without assuming the KPP condition.


heterogeneous reaction-diffusion equations, generalized transition waves, exponential decay

2010 Mathematics Subject Classification

35C07, 35K57

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