{"paper":{"title":"Finite time blow-up for an inhomogeneous parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaiqiang Zhang","submitted_at":"2026-07-13T07:01:52Z","abstract_excerpt":"We consider the inhomogeneous nonlinear heat equation \\[ \\partial_t u-\\Delta u=|u|^{p-1}u+f(x),\\qquad x\\in\\mathbb{R}^3,\\quad p>5, \\] where \\(f\\in L^\\infty\\cap C^{0,1}(\\mathbb{R}^3)\\). For every sufficiently large integer \\(n\\), we construct a codimension-\\(n\\) Lipschitz manifold of non-radial initial data whose corresponding solutions blow up in finite time and whose rescaled profiles converge to the prescribed self-similar profile \\(\\Phi_n\\) of the homogeneous equation.\n  The main novelty is to show that the finite-codimensional stability mechanism for self-similar blow-up, developed in the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11165","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/2607.11165/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"}