{"paper":{"title":"On the well-posedness of porous medium equations on general metric measure spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diwen Chang","submitted_at":"2026-07-23T03:32:22Z","abstract_excerpt":"We develop, on general metric measure spaces, a well-posedness theory for the Cauchy problem of the signed porous medium equation and its fast diffusion counterpart \\begin{equation*} \\partial_t u=\\mathcal{L}\\left(|u|^{m-1}u\\right), \\qquad m>0, \\end{equation*} where $\\mathcal{L}$ is the generator of a symmetric Dirichlet form. We prove that, for every initial datum $u_0\\in L^{m+1}(M,\\mu)$, there exists a unique function $u$ that weakly solves the equation in a suitable sense. The proof is based on the Rothe method and the theory of monotone operators and only uses the definition of the Dirichle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20894","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20894/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}