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Under some suitable conditions on the parameters of these SPDEs, we show that the second moment of their solutions blow up in finite time. This complements recent works of Khoshnevisan and his coauthors; see for instance Foondun and Khoshnevisan (2009), Foondun and Khoshnevisan (to appear, 2012) and Conus, Joseph, and Khoshnevisan, as well as those of Chow (Chow, 2009"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.4496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-22T13:36:05Z","cross_cats_sorted":[],"title_canon_sha256":"e988f80e2b49d073b95dfb988d42c8a0c3d9290fda07a0c7d367a148d9bae21c","abstract_canon_sha256":"c8f48f3e7c66cd1c30c8562113d048277a337e55f1762f975be011c35123f545"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:14.136776Z","signature_b64":"UXd+nExXP9sxWjjxich42QiBvWQ2XoNerFY1jwqZJuds3qMD6IB2Z36Gzpqr4TxdUbAVwkYnYKQF09VC5zPeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae08ceaf0a2cf0482bd2f3306f892313e42a7fc0c7092d810f6309942eb9fde2","last_reissued_at":"2026-05-18T03:48:14.136012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:14.136012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On non-existence of global solutions to a class of stochastic heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mohammud Foondun, Rana Parshad","submitted_at":"2012-08-22T13:36:05Z","abstract_excerpt":"We consider nonlinear parabolic SPDEs of the form $\\partial_t u=-(-\\Delta)^{\\alpha/2} u + b(u) +\\sigma(u)\\dot w$, where$\\dot w$ denotes space-time white noise. 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