{"paper":{"title":"Nonlocal dispersal equations in time-periodic media: principal spectral theory, bifurcation and asymptotic behaviors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Hoang-Hung Vo, Zhongwei Shen","submitted_at":"2017-04-03T01:47:21Z","abstract_excerpt":"This paper is devoted to the investigation of the following nonlocal dispersal equation $$ u_{t}(t,x)=\\frac{D}{\\sigma^m}\\left[\\int_{\\Omega}J_\\sigma(x-y)u(t,y)dy-u(t,x)\\right]+f(t,x,u(t,x)), \\quad t>0,\\quad x\\in\\overline{\\Omega}, $$ where $\\Omega\\subset\\mathbb{R}^{N}$ is a bounded and connected domain with smooth boundary, $m\\in[0,2)$, $D>0$ is the dispersal rate, $\\sigma>0$ characterizes the dispersal range, $J_{\\sigma}=\\frac{1}{\\sigma^{N}} J\\left(\\frac{\\cdot}{\\sigma}\\right)$ is the scaled dispersal kernel, and $f$ is a time-periodic nonlinear function of generalized KPP type. We first study t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00401","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"}