{"paper":{"title":"Long time behavior of random and nonautonomous Fisher-KPP equations. Part II. Transition fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rachidi B. Salako, Wenxian Shen","submitted_at":"2018-06-09T17:22:09Z","abstract_excerpt":"In the current series of two papers, we study the long time behavior of the following random Fisher-KPP equation $$ u_t =u_{xx}+a(\\theta_t\\omega)u(1-u),\\quad x\\in\\R, \\eqno(1) $$ where $\\omega\\in\\Omega$, $(\\Omega, \\mathcal{F},\\mathbb{P})$ is a given probability space, $\\theta_t$ is an ergodic metric dynamical system on $\\Omega$, and $a(\\omega)>0$ for every $\\omega\\in\\Omega$. We also study the long time behavior of the following nonautonomous Fisher-KPP equation, $$ u_t=u_{xx}+a_0(t)u(1-u),\\quad x\\in\\R, \\eqno(2) $$ where $a_0(t)$ is a positive locally H\\\"older continuous function. In the first p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03508","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"}