{"paper":{"title":"The diffusive competition problem with a free boundary in strong heterogeneous environment and weak heterogeneous environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengquan Li, Feng Wang, Qiaoling Chen","submitted_at":"2014-11-06T11:51:08Z","abstract_excerpt":"In this paper, we consider the diffusive competition problem consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and growth in $[0, \\infty)$, and $u$ exists initially in $[0, h_0)$, but invades into the environment with spreading front ${x=h(t)}$. To understand the effect of the dispersal rate $d_1$, the initial occupying habitat $h_0$, the initial density $u_{0}(x)$ of invasive species $(u)$, and the parameter $\\mu$ (the ratio of the invasion speed of the free boundary and the invasive species gradient at the expandi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1576","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"}