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Information Center for Mathematical Science

PAC

A short proof of the logarithmic Bramson correction in Fisher-KPP equations
Author Lenya Ryzhik (Stanford University)
Homepage Url http://math.stanford.edu/~ryzhik/
Coauthors Francois Hamel, James Nolen, Jean-Michel Roquejoffre
Abstract In this paper, we explain in simple PDE terms a famous result of Bramson about the loga- rithmic delay of the position of the solutions u(t; x) of Fisher-KPP reaction-di usion equations in R, with respect to the position of the travelling front with minimal speed. Our proof is based on the comparison of u to the solutions of linearized equations with Dirichlet boundary conditions at the position of the minimal front, with and without the logarithmic delay. Our analysis also yields the large-time convergence of the solutions u along their level sets to the pro le of the minimal travelling front.
Abstract Url http://math.stanford.edu/~ryzhik/hnrr1-submit.pdf