{"paper":{"title":"Stability properties for quasilinear parabolic equations with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Quoc-Hung Nguyen (LMPT)","submitted_at":"2014-09-04T18:37:37Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain of $\\mathbb{R}^{N}$, and $Q=\\Omega \\times(0,T).$ We study problems of the model type \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u=\\mu\\qquad\\text{in }Q,\\\\ {u}=0\\qquad\\text{on }\\partial\\Omega\\times(0,T),\\\\ u(0)=u_{0}\\qquad\\text{in }\\Omega, \\end{array} \\right. \\] where $p>1$, $\\mu\\in\\mathcal{M}_{b}(Q)$ and $u_{0}\\in L^{1}(\\Omega).$ Our main result is a \\textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\\longmapsto\\mathcal{A}(u)=$div$(A(x,t,\\nabla u))$\\textit{. }"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1518","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"}