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By comparing the coefficients of the polynomial, we could deduce the corresponding functional differential system of $(c(t),b(t),\\rho^{\\gamma-1}(0,t)).$ Then by skillfully applying the Hubble's transformation: \\begin{equ"},"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":"1012.2033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-09T15:37:06Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"b051a1f1515967cb9141113857a4503b4586e0f8bc450f6f309608c111512346","abstract_canon_sha256":"cfab1c55ac5d086b4993919e597286c90146b0085684fdd5d9cb701bc22f06b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:41.713997Z","signature_b64":"WtjALQmMFbAgLfvpRr5DbEZ5t4oEtI+VGgUnqslo3o1tD98jxYxphGUat0xxxkMJLyiVfR+yKy3r+VBjAtwoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8f1b2eac206cd0c088f02ec088bbf6731c1dee239c2cff5f138897f061378d5","last_reissued_at":"2026-05-18T04:11:41.713579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:41.713579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbational Blowup Solutions to the 1-dimensional Compressible Euler Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Manwai Yuen","submitted_at":"2010-12-09T15:37:06Z","abstract_excerpt":"We study the construction of analytical non-radially solutions for the 1-dimensional compressible adiabatic Euler equations in this article. 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