{"paper":{"title":"Some existence and regularity results for porous media and fast diffusion equations with a gradient term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boumediene Abdellaoui, Ireneo Peral, Magdalena Walias","submitted_at":"2012-10-18T09:27:11Z","abstract_excerpt":"In this paper we consider the problem $$(P)\\qquad \\{{array}{rclll} u_t-\\D u^m&=&|\\n u|^q +\\,f(x,t),&\\quad u\\ge 0 \\hbox{in} \\Omega_T\\equiv \\Omega\\times (0,T), u(x,t)&=&0 &\\quad \\hbox{on} \\partial\\Omega\\times (0,T) u(x,0)&=&u_0(x),&\\quad x\\in \\Omega {array}. $$ where $\\O\\subset \\ren$, $N\\ge 2$, is a bounded regular domain, $1<q\\le 2$, and $f\\ge 0$, $u_0\\ge 0$ are in a suitable class of functions.\n  We obtain some results for elliptic-parabolic problems with measure data related to problem $(P)$ that we use to study the existence of solutions to problem $(P)$ according with the values of the para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5062","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"}