We study the phenomenon of
invasion for heterogeneous reaction-diffusion
equations in periodic domains with monostable and combustion reaction
terms. We give an answer to a question raised by Berestycki, Hamel and
Nadirashvili concerning the connection between the speed of invasion and the
critical speed of fronts. To do so, we extend the classical Freidlin–Gärtner
formula to such equations and we derive some bounds on the speed of invasion
using estimates on the heat kernel. We also give geometric conditions on
the domain that ensure that the spreading occurs at the critical speed of
fronts.
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