{"paper":{"title":"Admissible wavefront speeds for a single species reaction-diffusion equation with delay","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Elena Trofimchuk, Sergei Trofimchuk","submitted_at":"2006-09-30T16:39:59Z","abstract_excerpt":"We consider equation $u_t(t,x) = \\Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*) $, when $g:\\R_+\\to \\R_+$ has exactly two fixed points: $x_1= 0$ and $x_2=\\kappa>0$. Assuming that $g$ is unimodal and has negative Schwarzian, we indicate explicitly a closed interval $\\mathcal{C} = \\mathcal{C}(h,g'(0),g'(\\kappa)) = [c_*,c^*]$ such that $(*)$ has at least one (possibly, nonmonotone) travelling front propagating at velocity $c$ for every $c \\in \\mathcal{C}$. Here $c_*>0$ is finite and $c^* \\in \\R_+ \\cup \\{+\\infty\\}$. Every time when $\\mathcal{C}$ is not empty, the minimal bound $c_*$ is sharp so that there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610025","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"}