{"paper":{"title":"On impulsive reaction-diffusion models in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.AP","authors_text":"Hao Wang, Mark Lewis, Mostafa Fazly","submitted_at":"2015-11-02T23:34:54Z","abstract_excerpt":"Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\\in \\mathbb Z^+$ \\begin{eqnarray*}\\label{}\n  \\ \\ \\ \\ \\ \\left\\{ \\begin{array}{lcl}\n  u^{(m)}_t = div(A\\nabla u^{(m)}-a u^{(m)}) + f(u^{(m)}) \\quad \\text{for} \\ \\ (x,t)\\in\\Omega\\times (0,1]\n  u^{(m)}(x,0)=g(N_m(x)) \\quad \\text{for} \\ \\ x\\in \\Omega\n  N_{m+1}(x):=u^{(m)}(x,1) \\quad \\text{for} \\ \\ x\\in \\Omega \\end{array}\\right.\n  \\end{eqnarray*} for functions $f,g$, a drift $a$ and a diffusion mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00743","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"}