{"paper":{"title":"On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro, Monica Marras, Nicola Pintus","submitted_at":"2019-04-24T11:13:10Z","abstract_excerpt":"In this paper we analyze the porous medium equation \\begin{equation}\\label{ProblemAbstract} \\tag{$\\Diamond$} %\\begin{cases} u_t=\\Delta u^m + a\\io u^p-b u^q -c\\lvert\\nabla\\sqrt{u}\\rvert^2 \\quad \\textrm{in}\\quad \\Omega \\times I,%\\\\ %u_\\nu-g(u)=0 & \\textrm{on}\\; \\partial \\Omega, t>0,\\\\ %u({\\bf x},0)=u_0({\\bf x})&{\\bf x} \\in \\Omega,\\\\ %\\end{cases} \\end{equation} where $\\Omega$ is a bounded and smooth domain of $\\R^N$, with $N\\geq 1$, and $I= [0,t^*)$ is the maximal interval of existence for $u$. The constants $a,b,c$ are positive, $m,p,q$ proper real numbers larger than 1 and the equation is compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10747","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"}