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Taliaferro","submitted_at":"2019-01-28T19:44:54Z","abstract_excerpt":"We investigate pointwise upper bounds for nonnegative solutions $u(x,t)$ of the nonlinear initial value problem \\begin{equation}\\label{0.1}\n  0\\leq(\\partial_t-\\Delta)^\\alpha u\\leq u^\\lambda \\quad\\text{ in }\\mathbb{R}^n \\times\\mathbb{R},\\,n\\geq1, \\end{equation} \\begin{equation}\\label{0.2}\n  u=0\\quad\\text{in }\\mathbb{R}^n\\times(-\\infty,0) \\end{equation} where $\\lambda$ and $\\alpha$ are positive constants. To do this we first give a definition---tailored for our study of this problem---of fractional powers of the heat operator $(\\partial_t-\\Delta)^\\alpha :Y\\to X$ where $X$ and $Y$ are linear spac"},"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":"1901.09964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-28T19:44:54Z","cross_cats_sorted":[],"title_canon_sha256":"9440bdef441705b5a933163d0be72c5e433129c05dbd0f523e5b3933d0d8b654","abstract_canon_sha256":"35f578292ad5307645948752ceac70a0d39e2668955d94dd6e96d648c30ea5eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:21.628511Z","signature_b64":"MYU0/i50ZyKYrj5morV84IA6puFmMHk5eL6NlNCStGNnpU2Tq6OO+q/pvXuRuHXjZ7xPlJYhT4iDE+s8a7hZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"547ee650b8d4daf0a802f09d7251eec20741d023a6d19e089bf31091df1f2760","last_reissued_at":"2026-05-17T23:50:21.627919Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:21.627919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise Bounds and Blow-up for Nonlinear Fractional Parabolic Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Steven D. 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