{"paper":{"title":"On distributional solutions of local and nonlocal problems of porous medium type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Espen R. Jakobsen, F\\'elix del Teso, J{\\o}rgen Endal","submitted_at":"2017-06-16T15:02:52Z","abstract_excerpt":"We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\\partial_tu-\\mathfrak{L}^{\\sigma,\\mu}[\\varphi(u)]=g(x,t)\\quad\\quad\\text{in}\\quad\\quad \\mathbb{R}^N\\times(0,T),$$ where $\\varphi$ is merely continuous and nondecreasing and $\\mathfrak{L}^{\\sigma,\\mu}$ is the generator of a general symmetric L\\'evy process. This means that $\\mathfrak{L}^{\\sigma,\\mu}$ can have both local and nonlocal parts like e.g. $\\mathfrak{L}^{\\sigma,\\mu}=\\Delta-(-\\Delta)^{\\frac12}$. New uniqueness results for bounded distributional solutions of this problem a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05306","kind":"arxiv","version":3},"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"}