{"paper":{"title":"The Fujita exponent across an interface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Ezzedine Mliki, Mohamed Majdoub","submitted_at":"2026-06-26T16:35:23Z","abstract_excerpt":"We consider the semilinear parabolic equation \\[ \\partial_t u = \\Delta u + 2\\mathfrak{q}\\,\\delta_{\\mathbb{S}}\\,\\nabla u + |u|^{p-1}u \\qquad \\text{in } (0,\\infty)\\times\\mathbb{R}^N, \\] where $|\\mathfrak{q}|\\le 1$, $p>1$, and $\\mathbb{S}$ is a fixed interface hyperplane.\n  Working in Lebesgue spaces, we first establish local well-posedness of mild solutions. This is achieved by combining Gaussian bounds for the associated fundamental solution with a contraction mapping argument adapted to the lack of spatial homogeneity induced by the interface term.\n  We then prove a sharp Fujita-type dichotomy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28248","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/2606.28248/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"}