{"paper":{"title":"Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Stuti Das","submitted_at":"2025-09-05T04:29:19Z","abstract_excerpt":"This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of \\cite{sanjitgarain,lazermc}. A central contribution of this work is the inclusion of a variable singular exponent. We examine both the purely singular and perturbed singular cases in the context of measure-valued data, where the source terms can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.04797","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/2509.04797/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"}