Luca Rossi – Propagation phenomena for KPP equations with general time-dependence

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Date(s) - 13 mars 2012

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We investigate the existence of generalized transition waves for reaction-diffusion equations with monostable nonlinearities depending in general way on time. It is well known that in the homogeneous case the family of speeds associated with traveling fronts is given by a right half-line. In collaboration with G. Nadin, we have extended this result by introducing a suitable notion of mean. As an application, we have derived the existence of random traveling waves when the nonlinearity is stationary ergodic. We further discuss some extensions to the case obtained by adding a space periodic dependence, which is a work in progress with L. Ryzhik.