{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QY3DTOMJF2MM6L5K76ANJBK2D7","short_pith_number":"pith:QY3DTOMJ","schema_version":"1.0","canonical_sha256":"863639b9892e98cf2faaff80d4855a1ff502488b7445299d0580ab3ac06da06d","source":{"kind":"arxiv","id":"1703.03299","version":1},"attestation_state":"computed","paper":{"title":"On fractional quasilinear parabolic problem with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amhed Attar, Boumediene Abdellaoui, Ireneo Peral, Rachid Bentifour","submitted_at":"2017-03-09T15:35:00Z","abstract_excerpt":"The aim goal of this paper is to treat the following problem \\begin{equation*} \\left\\{ \\begin{array}{rcll} u_t+(-\\D^s_{p}) u &=&\\dyle \\l \\dfrac{u^{p-1}}{|x|^{ps}} & \\text{ in } \\O_{T}=\\Omega \\times (0,T), \\\\ u&\\ge & 0 & \\text{ in }\\ren \\times (0,T), \\\\ u &=& 0 & \\text{ in }(\\ren\\setminus\\O) \\times (0,T), \\\\ u(x,0)&=& u_0(x)& \\mbox{ in }\\O, \\end{array}% \\right. \\end{equation*} where $\\Omega$ is a bounded domain containing the origin, $$ (-\\D^s_{p})\\, u(x,t):=P.V\\int_{\\ren} \\,\\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \\,dy$$ with $1<p<N, s\\in (0,1)$ and $f, u_0$ are non negative "},"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":"1703.03299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-09T15:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"e554c0c8d7f4f45bdf79d6aaa2d35a5ccad839ef3d1c6ab98c0e29ad51fc4dba","abstract_canon_sha256":"cb574dfc89942d7fbd3611aba1c6e8cd62879b4cdcc6cf45a15b50a6256ace05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:00.746780Z","signature_b64":"9P8XhG411vlz1TvFjkb97lxH+4TxyONfV+Tn11J9KDvgYJrVX2Ruu8Yygka7O9sxxUSv7pKBgZlbSZ0J+rEyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"863639b9892e98cf2faaff80d4855a1ff502488b7445299d0580ab3ac06da06d","last_reissued_at":"2026-05-18T00:49:00.746036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:00.746036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On fractional quasilinear parabolic problem with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amhed Attar, Boumediene Abdellaoui, Ireneo Peral, Rachid Bentifour","submitted_at":"2017-03-09T15:35:00Z","abstract_excerpt":"The aim goal of this paper is to treat the following problem \\begin{equation*} \\left\\{ \\begin{array}{rcll} u_t+(-\\D^s_{p}) u &=&\\dyle \\l \\dfrac{u^{p-1}}{|x|^{ps}} & \\text{ in } \\O_{T}=\\Omega \\times (0,T), \\\\ u&\\ge & 0 & \\text{ in }\\ren \\times (0,T), \\\\ u &=& 0 & \\text{ in }(\\ren\\setminus\\O) \\times (0,T), \\\\ u(x,0)&=& u_0(x)& \\mbox{ in }\\O, \\end{array}% \\right. \\end{equation*} where $\\Omega$ is a bounded domain containing the origin, $$ (-\\D^s_{p})\\, u(x,t):=P.V\\int_{\\ren} \\,\\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \\,dy$$ with $1<p<N, s\\in (0,1)$ and $f, u_0$ are non negative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03299","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":"1703.03299","created_at":"2026-05-18T00:49:00.746158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03299v1","created_at":"2026-05-18T00:49:00.746158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03299","created_at":"2026-05-18T00:49:00.746158+00:00"},{"alias_kind":"pith_short_12","alias_value":"QY3DTOMJF2MM","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QY3DTOMJF2MM6L5K","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QY3DTOMJ","created_at":"2026-05-18T12:31:39.905425+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/QY3DTOMJF2MM6L5K76ANJBK2D7","json":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7.json","graph_json":"https://pith.science/api/pith-number/QY3DTOMJF2MM6L5K76ANJBK2D7/graph.json","events_json":"https://pith.science/api/pith-number/QY3DTOMJF2MM6L5K76ANJBK2D7/events.json","paper":"https://pith.science/paper/QY3DTOMJ"},"agent_actions":{"view_html":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7","download_json":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7.json","view_paper":"https://pith.science/paper/QY3DTOMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03299&json=true","fetch_graph":"https://pith.science/api/pith-number/QY3DTOMJF2MM6L5K76ANJBK2D7/graph.json","fetch_events":"https://pith.science/api/pith-number/QY3DTOMJF2MM6L5K76ANJBK2D7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7/action/storage_attestation","attest_author":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7/action/author_attestation","sign_citation":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7/action/citation_signature","submit_replication":"https://pith.science/pith/QY3DTOMJF2MM6L5K76ANJBK2D7/action/replication_record"}},"created_at":"2026-05-18T00:49:00.746158+00:00","updated_at":"2026-05-18T00:49:00.746158+00:00"}