{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BZ2LRXG2DNJ3PYVF6BXAVZ2FRH","short_pith_number":"pith:BZ2LRXG2","schema_version":"1.0","canonical_sha256":"0e74b8dcda1b53b7e2a5f06e0ae74589de65ce36598a3cc6a70433e0f8fd4b4b","source":{"kind":"arxiv","id":"1709.01906","version":1},"attestation_state":"computed","paper":{"title":"Existence and stabilization results for a singular parabolic equation involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K. Sreenadh, Tuhina Mukherjee","submitted_at":"2017-09-06T17:29:13Z","abstract_excerpt":"In this article, we study the following parabolic equation involving the fractional Laplacian with singular nonlinearity \\begin{equation*}\n  \\quad (P_{t}^s) \\left\\{ \\begin{split}\n  \\quad u_t + (-\\Delta)^s u &= u^{-q} + f(x,u), \\;u >0\\; \\text{in}\\; (0,T) \\times \\Omega,\n  u &= 0 \\; \\mbox{in}\\; (0,T) \\times (\\mb R^n \\setminus\\Omega),\n  \\quad \\quad \\quad \\quad u(0,x)&=u_0(x) \\; \\mbox{in} \\; {\\mb R^n}, \\end{split} \\quad \\right. \\end{equation*} where $\\Omega$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Omega$, $n> 2s, \\;s \\in (0,1)$, $q>0$, ${q(2s-1)<(2s+1)}$, $u_0 \\in L^\\infty"},"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":"1709.01906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-06T17:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"dde0cbb8280b3a33de8d85f961289644e7d925d4dbac5efdfc5ae86348fde59f","abstract_canon_sha256":"183b3b5940a0da88e85925e5ea20b7b5583ee776c70fa051c25bf6f628c5843d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:54.080995Z","signature_b64":"hMso2/Bt89JDjM3aaudGd/u2oCLYvXvyybw63FuOBJWXzDPaVXq/LZ5M+ch04l0EtX+jKirJdyoV8IYa0niYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e74b8dcda1b53b7e2a5f06e0ae74589de65ce36598a3cc6a70433e0f8fd4b4b","last_reissued_at":"2026-05-18T00:35:54.080432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:54.080432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and stabilization results for a singular parabolic equation involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K. Sreenadh, Tuhina Mukherjee","submitted_at":"2017-09-06T17:29:13Z","abstract_excerpt":"In this article, we study the following parabolic equation involving the fractional Laplacian with singular nonlinearity \\begin{equation*}\n  \\quad (P_{t}^s) \\left\\{ \\begin{split}\n  \\quad u_t + (-\\Delta)^s u &= u^{-q} + f(x,u), \\;u >0\\; \\text{in}\\; (0,T) \\times \\Omega,\n  u &= 0 \\; \\mbox{in}\\; (0,T) \\times (\\mb R^n \\setminus\\Omega),\n  \\quad \\quad \\quad \\quad u(0,x)&=u_0(x) \\; \\mbox{in} \\; {\\mb R^n}, \\end{split} \\quad \\right. \\end{equation*} where $\\Omega$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Omega$, $n> 2s, \\;s \\in (0,1)$, $q>0$, ${q(2s-1)<(2s+1)}$, $u_0 \\in L^\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01906","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.01906","created_at":"2026-05-18T00:35:54.080525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01906v1","created_at":"2026-05-18T00:35:54.080525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01906","created_at":"2026-05-18T00:35:54.080525+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ2LRXG2DNJ3","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ2LRXG2DNJ3PYVF","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ2LRXG2","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH","json":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH.json","graph_json":"https://pith.science/api/pith-number/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/graph.json","events_json":"https://pith.science/api/pith-number/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/events.json","paper":"https://pith.science/paper/BZ2LRXG2"},"agent_actions":{"view_html":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH","download_json":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH.json","view_paper":"https://pith.science/paper/BZ2LRXG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01906&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/action/storage_attestation","attest_author":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/action/author_attestation","sign_citation":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/action/citation_signature","submit_replication":"https://pith.science/pith/BZ2LRXG2DNJ3PYVF6BXAVZ2FRH/action/replication_record"}},"created_at":"2026-05-18T00:35:54.080525+00:00","updated_at":"2026-05-18T00:35:54.080525+00:00"}