{"paper":{"title":"Sharp short and long time $\\mathbf L^{\\boldsymbol \\infty}$ bounds for solutions to porous media equations with Neumann boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Grillo, Matteo Muratori","submitted_at":"2012-06-22T22:20:36Z","abstract_excerpt":"We study a class of nonlinear diffusion equations whose model is the classical porous media equation on domains $\\Omega\\subseteq{\\mathbb R}^N$, $N\\ge3$, with homogeneous Neumann boundary conditions. Firstly we improve some known results in such model case, both as concerns sharp $L^{q_0}$-$L^\\infty$ regularizing properties of the evolution for short time and as concerns sharp long time asymptotics in the sense of $L^\\infty$ convergence of solutions to their mean value. The generality of the discussion allows to consider, almost at the same time, also weighted versions of the above equation pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5332","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"}