The logarithmic shift in Fisher-KPP type equations

Mercoledi' 7 Novembre 2012 - Jean-Michel Roquejoffre


Mercoledi' 7 Novembre 2012 alle ore 14:00 in aula 2BC30, Jean-Michel Roquejoffre (Universite' Paul Sabatier, Tolosa, Francia) terra' un seminario dal titolo "The logarithmic shift in Fisher-KPP type equations".

The issue here is the large time behaviour of the solutions of the Fisher-KPP equation. A well-known result of Kolmogorov-Petrovskii-Piskunov (1937) asserts that a solution whose initial value is the Heaviside function will converge, for large times, to a travelling wave of slowest speed. The profile of the solution is shifted by a strictly sub-linear in time quantity, that is not quantified in KPP's work. Much later, Bramson (1983) proved that the shift was actually logarithmic in time. We propose in this talk to revisit this result, and to discuss how it generalises to equations whose coefficients are inhomogeneous in space. Joint work with F. Hamel, J. Nolen and L. Ryzhik.

Rif. int. M. Bardi, C. Marchi, L. Rossi

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