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We prove blow-up in finite time in the subcritical range $p\\in(1,p_2(n)]$ and an existence result for $p>p_2(n)$, $n=2,3$. In this way we find the critical exponent for small data solutions to this problem. All these considerations lead to the conjecture $p_2(n)=p_0(n+2)$ for $n\\ge2$, where $p_0(n)"},"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":"1407.3449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-13T10:12:47Z","cross_cats_sorted":[],"title_canon_sha256":"414478827b85ca554514a623206fa449559ac281dd9fc0757d667cdfc4deb31f","abstract_canon_sha256":"49288342774d92d8534df502884c597a913724f69e8becc587b7092148e0e9cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:35.240798Z","signature_b64":"dHVRCsHCAJJt2FBzJT6I11f0P24vu+KqBUYJGaAaapTWrbXDt/WJYv+A/sNvDxVRKxib4sCgN3IxgQn5vZ6JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef5c25e69545a0bf16b43830a685169f878316a190009e206f7039ab537ac93","last_reissued_at":"2026-05-18T01:33:35.240243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:35.240243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From $p_0(n)$ to $p_0(n+2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcello D'Abbicco, Michael Reissig, Sandra Lucente","submitted_at":"2014-07-13T10:12:47Z","abstract_excerpt":"In this note we study the global existence of small data solutions to the Cauchy problem for the semi-linear wave equation with a not effective scale-invariant damping term, namely \\[ v_{tt}-\\triangle v + \\frac2{1+t}\\,v_t = |v|^p, \\qquad v(0,x)=v_0(x),\\quad v_t(0,x)=v_1(x), \\] where $p>1$, $n\\ge 2$. We prove blow-up in finite time in the subcritical range $p\\in(1,p_2(n)]$ and an existence result for $p>p_2(n)$, $n=2,3$. In this way we find the critical exponent for small data solutions to this problem. 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