(2) Production(s) de l'année 2017
|Reverse Cheeger inequality for planar convex sets |
Auteur(s): Parini E.
(Article) Publié: -Journal Of Convex Analysis, vol. 24 p. (2017)
|Sharp thresholds between finite spread and uniform convergence for a reaction-diffusion equation with oscillating initial data |
Auteur(s): Hamel F.
(Article) Publié: Journal Of Differential Equations, vol. 262 p.1461-1498 (2017)
Ref HAL: hal-01218913_v1
Ref Arxiv: 1510.06556
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
We investigate the large-time dynamics of solutions of multi-dimensional reaction-diffusion equations with ignition type nonlinearities. We consider solutions which are in some sense locally persistent at large time and initial data which asymptotically oscillate around the ignition threshold. We show that, as time goes to infinity, any solution either converges uniformly in space to a constant state, or spreads with a finite speed uniformly in all directions. Furthermore, the transition between these two behaviors is sharp with respect to the period vector of the asymptotic profile of the initial data. We also show the convergence to planar fronts when the initial data are asymptotically periodic in one direction.