Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

Uniqueness and stability properties of monostable pulsating fronts

François HamelLionel Roques — 2011

Journal of the European Mathematical Society

We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular,...

Symmetrization of functions and principal eigenvalues of elliptic operators

François HamelNikolai NadirashviliEmmanuel Russ

Séminaire Laurent Schwartz — EDP et applications

In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of n . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator - Δ + v · , for which the minimization problem is still well posed. Next, we deal with...

The speed of propagation for KPP type problems. I: Periodic framework

Henry BerestyckiFrançois HamelNikolai Nadirashvili — 2005

Journal of the European Mathematical Society

This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...

Page 1

Download Results (CSV)