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Such solutions are shown to exist only if the parameter $\\beta$ ranges in a bounded interval $(0,\\beta_*]$ which is in sharp contrast with well-known singular diffusion equations such as $\\partial_{t}\\phi-\\Delta_{p} \\phi=0$ when $p=2N"},"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":"1201.3196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-16T10:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"83b9f33585c373a422c676abb00aca2f6de3f2c61f7a1669cbe7b4fee8430d04","abstract_canon_sha256":"133f89c5e9190499a892ca682aaa657ca2ee22711a9779c7ebdc3691172b43ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:37.592125Z","signature_b64":"jyS+J8rT775doTzAm5pbPxbDmCMma5sSIhM2aln8JM/inugshAi3Ftq8vnrw7vmmy+AyAJqVF95JvGyEWwHZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef43122cbdb829cc72559e568cf3539a24719565ecfc7e46eacb7e55bd8bd1e4","last_reissued_at":"2026-05-18T03:00:37.588478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:37.588478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eternal solutions to a singular diffusion equation with critical gradient absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Laurencot (IMT), Razvan Gabriel Iagar (IMAR)","submitted_at":"2012-01-16T10:14:54Z","abstract_excerpt":"The existence of nonnegative radially symmetric eternal solutions of exponential self-similar type $u(t,x)=e^{-p\\beta t/(2-p)} f_\\beta(|x|e^{-\\beta t};\\beta)$ is investigated for the singular diffusion equation with critical gradient absorption\n\\partial_{t} u-\\Delta_{p} u+|\\nabla u|^{p/2}=0 \\quad \\;\\;\\hbox{in}\\;\\; (0,\\infty)\\times\\real^N\nwhere $2N/(N+1) < p < 2$. 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