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Salako, Wenxian Shen","submitted_at":"2017-01-10T15:19:56Z","abstract_excerpt":"We study traveling wave solutions of the following chemotaxis systems,$$\\begin{cases}u_t=\\Delta u-\\chi_1\\nabla(u\\nabla v_1)+\\chi_2\\nabla(u\\nabla v_2)+u(a-bu),\\ x\\in\\mathbb{R}^N\\\\ 0=\\Delta v_1-\\lambda_1v_1+\\mu_1u,\\ x\\in\\mathbb{R}^N,\\\\ 0=\\Delta v_2-\\lambda_2v_2+\\mu_2u,\\ x\\in\\mathbb{R}^N,\\end{cases}$$where $u(x,t), v_1(x,t)$ and $v_2(x,t)$ represent the population densities of a mobile species, a chemoattractant, and a chemo-repulsion, respectively. In an earlier work, we proved that there is a constant $K\\geq0$ such that if $b+\\chi_2\\mu_2>\\chi_1\\mu_1+K$, then the steady solution $(\\frac{a}{b},\\f"},"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":"1701.02633","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T15:19:56Z","cross_cats_sorted":[],"title_canon_sha256":"e19e1dca3e55d74525a15d9cbef01541cea1e01ff53df53cf2cc719ca17214f0","abstract_canon_sha256":"4f75c05380f65c229af37b4b41452a8507af4414221513330a61ea977528ce58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:54.815977Z","signature_b64":"B5XTynYA2HmEy8EzpF9y+jWX3fp3y9M5akPqdhelDYRSbEMRnwLZ6OjKgpkdUWrj2fJh0qCJER3SuUM9K5DACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d639a78fed49f26f1c1b1b27d53ad1cac42c3ecbd907891f5e485f9759a387f0","last_reissued_at":"2026-05-18T00:52:54.815438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:54.815438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rachidi B. 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