{"paper":{"title":"Wavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Evangelos Latos, Jing Li, Li Chen","submitted_at":"2017-01-24T13:59:33Z","abstract_excerpt":"The wavefronts of a nonlinear nonlocal bistable reaction-diffusion equation, \\begin{align*} \\frac{\\partial u}{\\partial t}=\\frac{\\partial^2u}{\\partial x^2}+u^2(1-J_\\sigma*u)-du,\\quad(t,x)\\in(0,\\infty)\\times\\mathbb R, \\end{align*} with $J_\\sigma(x)=(1/\\sigma)= J(x/\\sigma)$ and $ \\int_{\\mathbb R} J(x)dx=1 $ are investigated in this article. It is proven that there exists a $c_*(\\sigma)$ such that for all $c\\geq c_*(\\sigma)$, a monotone wavefront $(c,\\omega)$ can be connected by the two positive equilibrium points. On the other hand, there exists a $c^*(\\sigma)$ such that the model admits a semi-w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06875","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"}