{"paper":{"title":"Planar Traveling Waves For Nonlocal Dispersion Equation With Monostable Nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ming Mei, Rui Huang, Yong Wang","submitted_at":"2011-03-13T05:03:50Z","abstract_excerpt":"In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in $n$-dimensional space u_t - J\\ast u +u+d(u(t,x))= \\int_{\\mathbb{R}^n} f_\\beta (y) b(u(t-\\tau,x-y)) dy, u(s,x)=u_0(s,x),  s\\in[-\\tau,0], \\ x\\in \\mathbb{R}^n} \\] where the nonlinear functions $d(u)$ and $b(u)$ possess the monostable characters like Fisher-KPP type, $f_\\beta(x)$ is the heat kernel, and the kernel $J(x)$ satisfies ${\\hat J}(\\xi)=1-\\mathcal{K}|\\xi|^\\alpha+o(|\\xi|^\\alpha)$ for $0<\\alpha\\le 2$. After establishing the existence for both the planar traveling waves $\\phi(x\\cdot{\\bf e}+ct)$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2498","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"}