{"paper":{"title":"Monotone waves for non-monotone and non-local monostable reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk","submitted_at":"2015-09-16T02:02:27Z","abstract_excerpt":"We propose a criterion for the existence of monotone wavefronts in non-monotone and non-local monostable diffusive equations of the Mackey-Glass type. This extends recent results by Gomez et al proved for the particular case of equations with local delayed reaction. In addition, we demonstrate the uniqueness (up to a translation) of obtained monotone wavefront within the class of all monotone wavefronts (such a kind of conditional uniqueness was recently established for the non-local KPP-Fisher equation by Fang and Zhao). Moreover, we show that if delayed reaction is local then this uniqueness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04789","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"}