{"paper":{"title":"Existence and non-existence of transition fronts in mixed ignition-monostable media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Ma, Cole Graham, David Weber, Tau Shean Lim","submitted_at":"2017-05-09T23:07:10Z","abstract_excerpt":"We study transition fronts for one-dimensional reaction-diffusion equations with compactly perturbed ignition-monostable reactions. We establish an almost sharp condition on reactions which characterizes the existence and non-existence of fronts. In particular, we prove that a strong inhomogeneity in the reaction prevents formation of transition fronts, while a weak inhomogeneity gives rise to a front. Our work extends results and methods introduced by J. Nolen, J.M. Roquejoffre, L. Ryzhik, and A. Zlato\\v{s}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03563","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"}