{"paper":{"title":"Collapsing-tube type II blow-up for the energy-supercritical heat equation","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Manuel del Pino, Monica Musso, Yifu Zhou","submitted_at":"2026-07-18T09:47:07Z","abstract_excerpt":"We construct a new type II finite-time blow-up mechanism for the energy-supercritical heat equation \\[ u_t=\\Delta u+u^3, \\qquad n\\geq 5. \\] The solution is positive and blows up only at the origin, but in a highly anisotropic fashion. As $t\\nearrow T$, the solution concentrates in a thin tubular region around an $(n-4)$-dimensional sphere whose radius shrinks to zero at the self-similar scale \\[ \\xi_r(t)\\sim \\sqrt{2(n-4)(T-t)}. \\] At the same time, concentration takes place transversely to the sphere at the much smaller scale \\[ \\lambda(t)\\sim \\kappa_* \\frac{T-t}{|\\log(T-t)|^{\\frac n{n-2}}}, \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16733","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/2607.16733/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"}