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Assume that $b(t)$ is a nonnegative $C^{n,alpha}$ function and $a(x)$ is a nonnegative Gevrey function of order $s>1$ we prove that the Cauchy problem for $P$ is well-posed in the Gevrey class of any order $s<s'<1+(n+alpha)/2$."},"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":"1712.05253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T14:41:53Z","cross_cats_sorted":[],"title_canon_sha256":"cced5aff1816e1229aab85fabc90dc7ba75d72edeec928233642498dd8cd28a4","abstract_canon_sha256":"58d4beb41b0874a00b340cf6269f211fc34521c1986c13fc4eeed13907472368"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:04.976815Z","signature_b64":"Ow0hC0uLKbDVCfZKcwy37ZGEYgEfZQO4hYEg5asHbiudSwnb9Bp0lB6I108BoXSw7I27sytbrROqURap4Hr6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a26794103f3b3c8e996222042c487ae4e6f3b1233408c8d28f0597d50491d184","last_reissued_at":"2026-05-18T00:13:04.976067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:04.976067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Cauchy problem for $D_t^2-D_x(b(t)a(x))D_x$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ferruccio Colombini, Tatsuo Nishitani","submitted_at":"2017-12-14T14:41:53Z","abstract_excerpt":"We consider the Cauchy problem for second order differential operators with two independent variables $P=D_t^2-D_x(b(t)a(x))D_x$. 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