{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02633","kind":"arxiv","version":2},"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"}