{"paper":{"title":"Propagation phenomena for time heterogeneous KPP reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin, Luca Rossi","submitted_at":"2011-04-19T09:50:24Z","abstract_excerpt":"We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation $\\partial_t u -\\Delta u = f(t,u)$, $x\\in R^N$, $t\\in\\R$, where f=f(t,u) is a KPP monostable nonlinearity which depends in a general way on t. A typical f which satisfies our hypotheses is f(t,u)=m(t) u(1-u), with m bounded and having positive infimum. We first prove the existence of generalized transition waves (recently defined by Berestycki and Hamel, Shen) for a given class of speeds. As an application of this result, we obtain the existence of random transition waves when f is a random stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3686","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}