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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.03011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T18:40:41Z","cross_cats_sorted":[],"title_canon_sha256":"85b6946c3fcdf153d0a9f312a0b129735267260ed61164b2ee079f9751a20ee5","abstract_canon_sha256":"a9e9315476ef8c97f45c97b9392ab9a1b927510af65826b8be33b103abb3e288"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:34.030071Z","signature_b64":"ERAJrBZ12RMi5gHMtHoQXmT3p+Q2ma+cODcFo0Am2ejmuvDB+xQx6OsOoYpS42OXSNa4wrI5hFNo4iDZPjMFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d765e3f18742af56a942203c1d30ca63aee9e64525d30c978b1aa5384322d5cf","last_reissued_at":"2026-05-18T00:46:34.029300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:34.029300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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