{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:N6XUGHPZ25HGBCASOWWIG56BTZ","short_pith_number":"pith:N6XUGHPZ","schema_version":"1.0","canonical_sha256":"6faf431df9d74e60881275ac8377c19e5090058c1f46fe1312de975b2ac79c00","source":{"kind":"arxiv","id":"1707.08447","version":3},"attestation_state":"computed","paper":{"title":"Blowup solutions for a reaction-diffusion system with exponential nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Tej-Eddine Ghoul, Van Tien Nguyen","submitted_at":"2017-07-24T18:20:03Z","abstract_excerpt":"We consider the following parabolic system whose nonlinearity has no gradient structure: $$\\left\\{\\begin{array}{ll} \\partial_t u = \\Delta u + e^{pv}, \\quad & \\partial_t v = \\mu \\Delta v + e^{qu}, u(\\cdot, 0) = u_0, \\quad & v(\\cdot, 0) = v_0, \\end{array}\\right. \\quad p, q, \\mu > 0, $$ in the whole space $\\mathbb{R}^N$. We show the existence of a stable blowup solution and obtain a complete description of its singularity formation. The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. In particular, o"},"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":"1707.08447","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T18:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"4dbe5559744b8ac98a00161252b2fe0017342a0ce2d3d7bbacb690a82471f3ba","abstract_canon_sha256":"3b586234aeee26a690ee68d468904cc1f69856dc7cfd43362deafb2f855e8fe1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:36.675596Z","signature_b64":"n8WItc22cei8G1XgPt5qBsmSSQAxMG0Z1h175J6uU16zvS5UlzzbcwmkuRf1wtWLer/gJ8jhcpblByVeiiPaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6faf431df9d74e60881275ac8377c19e5090058c1f46fe1312de975b2ac79c00","last_reissued_at":"2026-05-18T00:26:36.674921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:36.674921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blowup solutions for a reaction-diffusion system with exponential nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Tej-Eddine Ghoul, Van Tien Nguyen","submitted_at":"2017-07-24T18:20:03Z","abstract_excerpt":"We consider the following parabolic system whose nonlinearity has no gradient structure: $$\\left\\{\\begin{array}{ll} \\partial_t u = \\Delta u + e^{pv}, \\quad & \\partial_t v = \\mu \\Delta v + e^{qu}, u(\\cdot, 0) = u_0, \\quad & v(\\cdot, 0) = v_0, \\end{array}\\right. \\quad p, q, \\mu > 0, $$ in the whole space $\\mathbb{R}^N$. We show the existence of a stable blowup solution and obtain a complete description of its singularity formation. The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. In particular, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08447","kind":"arxiv","version":3},"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":"1707.08447","created_at":"2026-05-18T00:26:36.675035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08447v3","created_at":"2026-05-18T00:26:36.675035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08447","created_at":"2026-05-18T00:26:36.675035+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6XUGHPZ25HG","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6XUGHPZ25HGBCAS","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6XUGHPZ","created_at":"2026-05-18T12:31:31.346846+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/N6XUGHPZ25HGBCASOWWIG56BTZ","json":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ.json","graph_json":"https://pith.science/api/pith-number/N6XUGHPZ25HGBCASOWWIG56BTZ/graph.json","events_json":"https://pith.science/api/pith-number/N6XUGHPZ25HGBCASOWWIG56BTZ/events.json","paper":"https://pith.science/paper/N6XUGHPZ"},"agent_actions":{"view_html":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ","download_json":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ.json","view_paper":"https://pith.science/paper/N6XUGHPZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08447&json=true","fetch_graph":"https://pith.science/api/pith-number/N6XUGHPZ25HGBCASOWWIG56BTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/N6XUGHPZ25HGBCASOWWIG56BTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ/action/storage_attestation","attest_author":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ/action/author_attestation","sign_citation":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ/action/citation_signature","submit_replication":"https://pith.science/pith/N6XUGHPZ25HGBCASOWWIG56BTZ/action/replication_record"}},"created_at":"2026-05-18T00:26:36.675035+00:00","updated_at":"2026-05-18T00:26:36.675035+00:00"}