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Thus, using a frequency domain method inspired from \\cite{BT}, we prove the polynomial decays of its total energy with $t^{-\\nicefrac{1}{2}}$ decay rate."},"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":"1801.04746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T11:35:05Z","cross_cats_sorted":[],"title_canon_sha256":"38e0985521f976a0b66bd2e724ba832cd81a06d597830764180081b999229cfc","abstract_canon_sha256":"de5d693aa3e800a914cc1c64e1714df924568fe48b7310f63df9878c882b0795"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:03.395489Z","signature_b64":"kMtvXrr5Btuw1xBd5BOwqPqMn3dd2r9DVX9evxkQBwnKmds/rb/rJyqsOe+Z5hcJjYGhJsS0b0/YPnSGTgmgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a36bac39c42dcb3efbae5c2c46803f2e129aa717fa6779261762cfd906eb9b6","last_reissued_at":"2026-05-18T00:26:03.394838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:03.394838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A frequency approach for stabilization of one-dimensional degenerate wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Akram Ben Aissa, Ali Segher Kadai, Mohamed Ferhat","submitted_at":"2018-01-15T11:35:05Z","abstract_excerpt":"In this paper, we are concerned with the study of stabilization problem for the following strongly degenerate wave equation in one space dimension $$w_{tt}(x,t)-\\left(x^\\alpha w_x(x,t)\\right)_x=0$$ where ${\\bf\\alpha\\in [1,2)}$. 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