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On the one hand we will prove a global (in time) existence result for \\eqref{CP abstract} under suitable assumptions on the coefficients $\\mu_1, \\mu_2^2$ of the damping and the mass term a"},"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":"1708.00738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-02T13:32:46Z","cross_cats_sorted":[],"title_canon_sha256":"3582cdc92556cca575755086108c8bc413e13dc8e64d8c8ee85a09c2ffb1810c","abstract_canon_sha256":"6b4d8a810bf162d6b4caf56df0bd90bbeefa82ac40eb71a9f319d4f43fbe05dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:08.792282Z","signature_b64":"h9QryHvisiTWsA6EjDbLKGT6oucGp9PYb15aIqf84qyuQuYZfZFBHG/ublmeaEg8WezpiNWTR6XKtEMm/NpyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6f22fe2b08731a36877d01b0ee6c1b02ce3b570600c2d0077b16f4efe52fccd","last_reissued_at":"2026-05-17T23:58:08.791824Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:08.791824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Palmieri","submitted_at":"2017-08-02T13:32:46Z","abstract_excerpt":"In this paper we consider the following Cauchy problem for the semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity: \\begin{align}\\label{CP abstract} \\begin{cases} u_{tt}-\\Delta u+\\dfrac{\\mu_1}{1+t} u_t+\\dfrac{\\mu_2^2}{(1+t)^2}u=|u|^p, \\\\ u(0,x)=u_0(x), \\,\\, u_t(0,x)=u_1(x), \\end{cases}\\tag{$\\star$} \\end{align} where $\\mu_1, \\mu_2^2$ are nonnegative constants and $p>1$. 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