{"paper":{"title":"The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yihong Du, Zhigui Lin","submitted_at":"2013-03-03T03:31:20Z","abstract_excerpt":"In this paper we consider the diffusive competition model consisting of an invasive species with density $u$ and a native species with density $v$, in a radially symmetric setting with free boundary. We assume that $v$ undergoes diffusion and growth in $\\R^N$, and $u$ exists initially in a ball $\\{r<h(0)\\}$, but invades into the environment with spreading front $\\{r=h(t)\\}$, with $h(t)$ evolving according to the free boundary condition $h'(t)=-\\mu u_r(t, h(t))$, where $\\mu>0$ is a given constant and $u(t,h(t))=0$. Thus the population range of $u$ is the expanding ball $\\{r<h(t)\\}$, while that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0454","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"}