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Moreover, $f$ is a continuous monotone increasing positive bounded function with $f(0)=0$ and the initial data $u_0(x)$ is bounded smooth and compactly supported. Thus, through an homotopy argu"},"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":"1903.09552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-22T15:19:28Z","cross_cats_sorted":[],"title_canon_sha256":"a7bf0ddca903610227b147413842eb4c0af3b9069ae04110701a2cac31295362","abstract_canon_sha256":"18e1825074a46859c23d51b7df8b923df293717e88b7f905a4c4530653f9d962"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.277428Z","signature_b64":"Fo/5RWe2Zy4hKqy/VHJoGFvA627+OYwUOuhvek9hgHSp3yj6qHr7g0jD8BdyTjsyezWGl04Tn/yY2C30iiMnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72d8305997862550d78f3cf6c71cc984ab608a8067da49d6985800b03f1fea0c","last_reissued_at":"2026-05-17T23:50:39.276853Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.276853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopy regularization for a high-order parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Pablo \\'Alvarez-Caudevilla","submitted_at":"2019-03-22T15:19:28Z","abstract_excerpt":"In this work we study the solvability of the Cauchy Problem for a quasilinear degenerate high-order parabolic equation \\begin{equation*}\n  \\left\\{\n  \\begin{tabular}{lcl}\n  $u_t=(-1)^{m-1}\\nabla\\cdot(f^n(|u|)\\nabla\\Delta^{m-1}u)$ & &in $\\mathbb{R}^N\\times\\mathbb{R}_+$,\n  $u(x,0)=u_0(x)$& & in $\\mathbb{R}^N$,\n  \\end{tabular}\n  \\right. \\end{equation*} with $m\\in\\mathbb{N},\\ m>1$ and $n>0$ a fixed exponent. Moreover, $f$ is a continuous monotone increasing positive bounded function with $f(0)=0$ and the initial data $u_0(x)$ is bounded smooth and compactly supported. 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