{"paper":{"title":"Parabolic-elliptic chemotaxis model with space-time dependent logistic sources on $\\mathbb{R}^N$. III. Transition fronts","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":"2018-11-05T06:09:58Z","abstract_excerpt":"The current work is the third of a series of three papers devoted to the study of asymptotic dynamics in the space-time dependent logistic source chemotaxis system, $$ \\begin{cases} \\partial_tu=\\Delta u-\\chi\\nabla\\cdot(u\\nabla v)+u(a(x,t)-b(x,t)u),\\quad x\\in R^N,\\cr 0=\\Delta v-\\lambda v+\\mu u ,\\quad x\\in R^N, \\end{cases} (0.1) $$ where $N\\ge 1$ is a positive integer, $\\chi, \\lambda$ and $\\mu$ are positive constants, the functions $a(x,t)$ and $b(x,t)$ are positive and bounded. In the first of the series, we studied the phenomena of persistence, and the asymptotic spreading for solutions. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01525","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"}