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After presenting $L^m-L^r$ estimates with $1\\leq m\\leq r\\leq \\infty$ of solutions to the corresponding linearized problem with vanishing right-hand side, we prove the existence of global in time solutions to the"},"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":"1809.07525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-20T08:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"4728287c8c6391bc3dae6894a16d70f3ab13a1612083fa0e1acb672c4d86a9cd","abstract_canon_sha256":"a18375e57084a843e7fef4f80bbeeb3af12141e5917eb9ce6755edeb75d1cd48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:55.340992Z","signature_b64":"shH/WxMvGFh2IxYX9bawlG7steBS4Dymj4xtsWlcZIaqtrG9YgWh4R3U0fMSWQdkHZVKEV3cSYZdD9S6H4oTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053702f64515acf5920d21c3153cd17f4c1e9f7ed6973add44e0e410d6432065","last_reissued_at":"2026-05-18T00:03:55.340380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:55.340380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An application of $L^m-L^r$ estimates to weakly coupled systems of semilinear viscoelastic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenhui Chen, Yan Liu","submitted_at":"2018-09-20T08:30:53Z","abstract_excerpt":"We consider weakly coupled systems of semilinear viscoelastic wave equations with different power source nonlinearities in $\\mathbb{R}^n$, $n\\geq1$ as follows: \\begin{equation*} \\left\\{\\begin{aligned} &u_{tt}-\\Delta u+g\\ast\\Delta u+u_t=|\\partial_t^{\\ell}v|^p,\\\\ &v_{tt}-\\Delta v+g\\ast\\Delta v+v_t=|\\partial_t^{\\ell}u|^q,\\\\ \\end{aligned}\\right. \\end{equation*} with $\\ell=0,1$ and $p,q>1$. 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