{"paper":{"title":"On traveling wave solutions in full parabolic Keller-Segel chemotaxis systems with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"R. B. Salako, W. Shen","submitted_at":"2019-01-07T23:19:33Z","abstract_excerpt":"This paper is concerned with traveling wave solutions of the following full parabolic Keller-Segel chemotaxis system with logistic source, \\begin{equation} \\begin{cases} u_t=\\Delta u -\\chi\\nabla\\cdot(u\\nabla v)+u(a-bu),\\quad x\\in\\mathbb{R}^N \\cr \\tau v_t=\\Delta v-\\lambda v +\\mu u,\\quad x\\in \\mathbb{R}^N, \\end{cases}(1) \\end{equation} where $\\chi, \\mu,\\lambda,a,$ and $b$ are positive numbers, and $\\tau\\ge 0$. Among others, it is proved that if $b>2\\chi\\mu$ and $\\tau \\geq \\frac{1}{2}(1-\\frac{\\lambda}{a})_{+} ,$ then for every $c\\ge 2\\sqrt{a}$, (1) has a traveling wave solution $(u,v)(t,x)=(U^{\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02727","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"}