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The growth of the monotone vector field $A$ is controlled by a generalized fully anisotropic $N$-function $M:[0,T)\\times\\Omega\\times\\mathbb{R}^N\\to[0,\\infty)$ inhomogeneous in time and space, and un"},"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":"1806.06711","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-15T11:03:19Z","cross_cats_sorted":[],"title_canon_sha256":"ad6c03e445674f7f769ed5bf1f95942a1b494a637a58973c5919f522bbd00272","abstract_canon_sha256":"8d85abfefe50d290dca117c3dba552395e0cac618987689ba30cafee50de0b60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:30.356588Z","signature_b64":"HfzIA9sjMgwUKWfqo04m8bm4ABxfuSWQ3s14ck5yDFlqw6bqTTIvxRm2uGVhCoXa4YOkcf75ORHHe6vCeJyyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fdfd15392db8282eb9e1d5d375e09b9fc1820810fcf844b91ac9635f20a3f8f","last_reissued_at":"2026-05-17T23:46:30.355898Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:30.355898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Zatorska-Goldstein, Iwona Chlebicka, Piotr Gwiazda","submitted_at":"2018-06-15T11:03:19Z","abstract_excerpt":"We study a general nonlinear parabolic equation on a Lipschitz bounded domain in $\\mathbb{R}^N$, \\begin{equation*} \\left\\{\\begin{array}{l l} \\partial_t u-\\mathrm{div} A(t,x,\\nabla u)= f(t,x)&\\text{in}\\ \\ \\Omega_T,\\\\ u(t,x)=0 &\\ \\mathrm{ on} \\ (0,T)\\times\\partial\\Omega,\\\\ u(0,x)=u_0(x)&\\text{in}\\ \\Omega, \\end{array}\\right. \\end{equation*} with $f\\in L^\\infty(\\Omega_T)$ and $u_0\\in L^\\infty(\\Omega)$. 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