{"paper":{"title":"Properties of solutions to porous medium problems with different sources and boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro, Nicola Pintus, Tongxing Li","submitted_at":"2018-05-19T08:09:01Z","abstract_excerpt":"In this paper we study nonnegative and classical solutions $u=u(\\nx,t)$ to porous medium problems of the type \\begin{equation}\\label{ProblemAbstract} \\tag{$\\Diamond$} \\begin{cases} u_t=\\Delta u^m + g(u,|\\nabla u|) & {\\bf x} \\in \\Omega, t\\in I,\\\\ %u_\\nu+hu=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 $N\\geq 1$, $I=(0,t^*)$ is the maximal interval of existence of $u$, $m>1$ and $u_0(\\nx)$ is a nonngative and sufficiently regular function. The problem is equipped w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07543","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"}