{"paper":{"title":"Stability of semi-wavefronts for delayed reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abraham Solar","submitted_at":"2017-04-10T18:40:41Z","abstract_excerpt":"This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \\in \\mathbb{R},\\ t >0,$ where $h>0$ and the reaction term $g: \\mathbb{R}_+ \\to \\mathbb{R}_+$ has exactly two fixed points (zero and $\\kappa >0$). Under certain condition on the derivative of $g$ at $\\kappa$, the global stability of fast wavefronts is proved. Also, the stability of the $leading \\ edge$ of semi-wavefronts for $(*)$ with $g$ satisfying $g(u)\\leq g'(0)u, u\\in\\R_+,$ is established"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03011","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"}