{"paper":{"title":"Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anne-Charline Coulon, Jean-Michel Roquejoffre","submitted_at":"2011-11-02T07:26:26Z","abstract_excerpt":"We study the Fisher-KPP equation with a fractional laplacian of order {\\alpha} \\in (0, 1). We know that the stable state invades the unstable one at constant speed for {\\alpha} = 1, and at an exponential in time velocity for {\\alpha} \\in (0, 1). The transition between these two different speeds is examined in this paper. We prove that during a time of the order - ln(1 - {\\alpha}), the propagation is linear and then it is exponential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0408","kind":"arxiv","version":1},"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"}