{"paper":{"title":"Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: the subcritical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel Salort, Joana Terra, Noem\\'i Wolanski","submitted_at":"2014-04-11T21:16:52Z","abstract_excerpt":"In this paper we continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption \\begin{align} \\begin{cases} u_t = \\mathcal{L} u-u^p\\quad& \\mbox{in}\\quad \\mathbb R^N\\times(0,\\infty),\\\\ u(x,0) = u_0(x)\\quad& \\mbox{in}\\quad \\mathbb R^N, \\end{cases} \\end{align} where $p>1$, $u_0\\ge0$ and bounded and $$ \\mathcal{L} u(x,t)=\\int J(x-y)\\left(u(y,t)-u(x,t)\\right)\\,dy $$ with $J\\in C_0^{\\infty}(\\mathbb R^N)$, radially symmetric, $J\\geq 0$ with $\\int J=1$.\n  Our assumption on the initial datum is that $0\\le u_0\\in L^\\infty(\\mathbb R^N)$ and $$ |x|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3226","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"}