Propagation phenomena for KPP equations with general time-dependence

Date/heure
Date(s) - 13/03/2012
10 h 00 min - 11 h 00 min

Catégories Pas de Catégories

$We\; investigate\; the\; existence\; of\; generalized\; transition\; waves\; for\; reaction-diffusion\; equations\; with\; monostable\; nonlinearities\; depending\; in\; general\; way\; on\; time.\; It\; is\; well\; known\; that\; in\; the\; homogeneous\; case\; the\; family\; of\; speeds\; associated\; with\; traveling\; fronts\; is\; given\; by\; a\; right\; half-line.\; In\; collaboration\; with\; G.\; Nadin,\; we\; have\; extended\; this\; result\; by\; introducing\; a\; suitable\; notion\; of\; mean.\; As\; an\; application,\; we\; have\; derived\; the\; existence\; of\; random\; traveling\; waves\; when\; the\; nonlinearity\; is\; stationary\; ergodic.\; We\; further\; discuss\; some\; extensions\; to\; the\; case\; obtained\; by\; adding\; a\; space\; periodic\; dependence,\; which\; is\; a\; work\; in\; progress\; with\; L.\; Ryzhik.$