{"paper":{"title":"Entire Solutions of the Fisher-KPP Equation on the Half Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bendong Lou, Junfan Lu, Yoshihisa Morita","submitted_at":"2018-09-02T08:01:20Z","abstract_excerpt":"In this paper we study the entire solutions of the Fisher-KPP equation $u_t=u_{xx}+f(u)$ on the half line $[0,\\infty)$ with Dirichlet boundary condition at $x=0$. (1). For any $c\\geq 2\\sqrt{f'(0)}$, we show the existence of an entire solution $\\mathcal{U}^c(x,t)$ which connects the traveling wave solution $\\phi^c(x+ct)$ at $t=-\\infty$ and the unique positive stationary solution $V(x)$ at $t=+\\infty$; (2). We also construct an entire solution $\\mathcal{U}(x,t)$ which connects the solution of $\\eta_t =f(\\eta)$ at $t=-\\infty$ and $V(x)$ at $t=+\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00308","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"}