{"paper":{"title":"The hair-trigger effect for a class of nonlocal nonlinear equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Dmitri Finkelshtein, Pasha Tkachov","submitted_at":"2017-02-26T20:11:50Z","abstract_excerpt":"We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on $\\mathbb{R}^d$ which have only two constant stationary solutions, $0$ and $\\theta>0$. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to $\\infty$) to $\\theta$ locally uniformly in $\\mathbb{R}^d$. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08076","kind":"arxiv","version":3},"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"}