{"paper":{"title":"Global classical solutions, stability of constant equilibria, and spreading speeds in attraction-repulsion chemotaxis systems with logistic source on $\\mathbb{R}^{N}$","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":"2016-12-03T05:01:01Z","abstract_excerpt":"We consider the following chemotaxis systems $$\\begin{cases}u_t=\\Delta u-\\chi_1\\nabla(u\\nabla v_1)+\\chi_2\\nabla(u\\nabla v_2)+u(a-bu),\\ \\ x\\in\\mathbb R^N,t>0,\\\\0=(\\Delta-\\lambda_1I)v_1+\\mu_1u,\\ \\ x\\in\\mathbb R^N,t>0,\\\\0=(\\Delta-\\lambda_2I)v_2+\\mu_2u,\\ \\ \\text{in}\\ x\\in\\mathbb R^N,\\ t>0,\\\\u(\\cdot,0)=u_0,\\ \\ x\\in\\mathbb R^N,\\end{cases}$$where $\\chi_i,\\ \\lambda_i,\\ \\mu_i,\\ i=1,2$ and $a,\\ b$ are positive constant real numbers and $N$ is a positive integer. Under some conditions on the parameters, we prove the global existence and boundedness of classical solutions $(u(x,t;u_0),v_1(x,t;u_0),v_2(x,t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00924","kind":"arxiv","version":3},"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"}