{"paper":{"title":"Effects of localized spatial variations on the uniform persistence and spreading speeds of time periodic two species competition systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liang Kong, Tung Nguyen, Wenxian Shen","submitted_at":"2018-03-14T14:46:40Z","abstract_excerpt":"The current paper is devoted to the study of two species competition systems of the form \\begin{equation*} \\begin{cases} u_t(t,x)= \\mathcal{A} u+u(a_1(t,x)-b_1(t,x)u-c_1(t,x)v),\\quad x\\in\\RR\\cr v_t(t,x)= \\mathcal{A} v+ v(a_2(t,x)-b_2(t,x)u-c_2(t,x) v),\\quad x\\in\\RR \\end{cases} \\end{equation*} where $\\mathcal{A}u=u_{xx}$, or $(\\mathcal{A}u)(t,x)=\\int_{\\RR}\\kappa(y-x)u(t,y)dy-u(t,x)$ ($\\kappa(\\cdot)$ is a smooth non-negative convolution kernel supported on an interval centered at the origin), $a_i(t+T,x)=a_i(t,x)$, $b_i(t+T,x)=b_i(t,x)$, $c_i(t+T,x)=c_i(t,x)$, and $a_i$, $b_i$, and $c_i$ ($i=1,2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05322","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"}