%0 Journal Article
%T Front blocking and propagation in cylinders with varying cross section
%+ Centre d'Analyse et de Mathématique sociales (CAMS)
%+ Laboratoire Jacques-Louis Lions (LJLL)
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Berestycki, Henri
%A Bouhours, Juliette
%A Chapuisat, Guillemette
%Z Bourse de doctorat "Bourse hors DIM" de la "Région Ile de France" de Juliette BouhoursNSF FRG grant DMS-1065979 de Henri Berestycki
%Z NONLOCAL ANR-14-CE25-0013
%< avec comité de lecture
%@ 0944-2669
%J Calculus of Variations and Partial Differential Equations
%I Springer Verlag
%V 55
%N 3
%P 55-44
%8 2016-06
%D 2016
%Z 1501.01326
%R 10.1007/s00526-016-0962-2
%K Reaction-diffusion equations
%K travelling waves
%K invasion fronts
%K bistable equation
%K blocking
%K propagation
%K stationary solutions
%Z MSC: 35B08, 35B30, 35B40,35C07, 35K57, 92B05, 92C20
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X In this paper we consider a bistable reaction-diffusion equation in unbounded domains and we investigate the existence of propagation phenomena, possibly partial, in some direction or, on the contrary, of blocking phenomena. We start by proving the well-posedness of the problem. Then we prove that when the domain has a decreasing cross section with respect to the direction of propagation there is complete propagation. Further, we prove that the wave can be blocked as it comes to an abrupt geometry change. Finally we discuss various general geometrical properties that ensure either partial or complete invasion by 1. In particular, we show that in a domain that is "star-shaped" with respect to an axis, there is complete invasion by 1.
%G English
%2 https://hal.science/hal-01101159/document
%2 https://hal.science/hal-01101159/file/BBC_150106.pdf
%L hal-01101159
%U https://hal.science/hal-01101159
%~ UNIV-PARIS7
%~ UPMC
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ EHESS
%~ LJLL
%~ OPENAIRE
%~ I2M
%~ TDS-MACS
%~ USPC
%~ UPMC_POLE_1
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ SU-TI
%~ ALLIANCE-SU
%~ CAMS