{"paper":{"title":"Global continuation of monotone wavefronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Adrian Gomez, Sergei Trofimchuk","submitted_at":"2012-10-24T01:32:58Z","abstract_excerpt":"In this paper, we answer the question about the criteria of existence of monotone travelling fronts $u = \\phi(\\nu \\cdot x+ct), \\phi(-\\infty) =0, \\phi(+\\infty) = \\kappa,$ for the monostable (and, in general, non-quasi-monotone) delayed reaction-diffusion equations $u_t(t,x) - \\Delta u(t,x) = f(u(t,x), u(t-h,x)).$ $C^{1,\\gamma}$-smooth $f$ is supposed to satisfy $f(0,0) = f(\\kappa,\\kappa) =0$ together with other monostability restrictions. Our theory covers the two most important cases: Mackey-Glass type diffusive equations and KPP-Fisher type equations. The proofs are based on a variant of Hale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6419","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"}