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It is proven that there exists a $c_*(\\sigma)$ such that for all $c\\geq c_*(\\sigma)$, a monotone wavefront $(c,\\omega)$ can be connected by the two positive equilibrium points. On the other hand, there exists a $c^*(\\sigma)$ such that the model admits a semi-w"},"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":"1701.06875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-24T13:59:33Z","cross_cats_sorted":[],"title_canon_sha256":"122e6116309d90fcb144294085bef22a0461430b286a5a8c351dba9647d52c1c","abstract_canon_sha256":"7ab3519c02ae96902c10e20b72fa632e2d62bfb61a13660128ed42428e962257"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:10.256081Z","signature_b64":"xynIMhPL1N+nI2/5ETeiUjvsP8oK6lcL3glPFblIlZG5j2XonhReYLks8CjpKLF23nz6ULfsaT5NJEAGyh4zCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"894197b2c90c1ce6396296aef23bbdbefd2d85a1cfc5770b594f7bd81642fc1d","last_reissued_at":"2026-05-18T00:52:10.255572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:10.255572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Evangelos Latos, Jing Li, Li Chen","submitted_at":"2017-01-24T13:59:33Z","abstract_excerpt":"The wavefronts of a nonlinear nonlocal bistable reaction-diffusion equation, \\begin{align*} \\frac{\\partial u}{\\partial t}=\\frac{\\partial^2u}{\\partial x^2}+u^2(1-J_\\sigma*u)-du,\\quad(t,x)\\in(0,\\infty)\\times\\mathbb R, \\end{align*} with $J_\\sigma(x)=(1/\\sigma)= J(x/\\sigma)$ and $ \\int_{\\mathbb R} J(x)dx=1 $ are investigated in this article. It is proven that there exists a $c_*(\\sigma)$ such that for all $c\\geq c_*(\\sigma)$, a monotone wavefront $(c,\\omega)$ can be connected by the two positive equilibrium points. 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