{"paper":{"title":"Logarithmic corrections in Fisher-KPP type Porous Medium Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando Quiros, Maolin Zhou, Yihong Du","submitted_at":"2018-06-06T06:17:48Z","abstract_excerpt":"We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\\infty(\\mathbb{R}^N)\\setminus\\{0\\}$: \\begin{equation} \\label{eq:abstract} \\tag{$\\star$}u_t=\\Delta u^m+u-u^2\\quad\\text{in }Q:=\\mathbb{R}^N\\times\\mathbb{R}_+,\\qquad u(\\cdot,0)=u_0\\quad\\text{in }\\mathbb{R}^N, \\end{equation} with $m>1$. It is well known that the spatial support of the solution $u(\\cdot, t)$ to this problem remains bounded for all time $t>0$. In spatial dimension one it is known that there is a minimal speed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02022","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"}