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Ignat","submitted_at":"2012-07-11T09:01:53Z","abstract_excerpt":"In this paper we obtain bounds for the decay rate in the $L^r (\\rr^d)$-norm for the solutions to a nonlocal and nolinear evolution equation, namely, $$u_t(x,t) = \\int_{\\rr^d} K(x,y) |u(y,t)- u(x,t)|^{p-2} (u(y,t)- u(x,t)) \\, dy, $$ with $ x \\in \\rr^d$, $ t>0$. Here we consider a kernel $K(x,y)$ of the form $K(x,y)=\\psi (y-a(x))+\\psi(x-a(y))$, where $\\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ is a linear function $a(x)= Ax$. To obtain the decay rates we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form $ T(u) = -"},"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":"1207.2565","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-11T09:01:53Z","cross_cats_sorted":[],"title_canon_sha256":"0bd288f31ef1864e29e09ca3e4b2f43aaa41afb4c53b2603a754a34292216abb","abstract_canon_sha256":"c23533f2ea475f67e93e277fb60275d29f9423c1d27fcd1bf9154432192525d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:19.665774Z","signature_b64":"jNjGDNGrG9cQ2wxWO5qWZM+T9JObt4JuRuIGis56/QKLN0NZXwlnc7tnzQlYF9BHVcmmrjulQADj7zOv6/FVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c34019d78c30410f6ca9c76f22642c72ba43b7ff9827255e104a228fefdaaf5d","last_reissued_at":"2026-05-18T03:28:19.665234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:19.665234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decay estimates for nonlinear nonlocal diffusion problems in the whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angel San Antolin, Dami\\'an Pinasco, Julio D. 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