{"paper":{"title":"Evolution equations of p-Laplace type with absorption or source terms and 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":"2014-09-04T18:38:40Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain of $\\mathbb{R}^{N}$, and $Q=\\Omega \\times(0,T).$ We consider problems\\textit{ }of the type % \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u\\pm\\mathcal{G}(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 ${\\Delta_{p}}$ is the $p$-Laplacian, $\\mu$ is a bounded Radon measure, $u_{0}\\in L^{1}(\\Omega),$ and $\\pm\\mathcal{G}(u)$ is an absorption or a source term$.$ In the model case $\\mathcal{G}(u)=\\pm\\left\\vert u\\right\\vert ^{q-1}u$ $(q>p-1),$ or $\\mathcal{G}$ has an ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1520","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"}