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We study the problem \\begin{equation} (P)\\left\\{ \\begin{array}{lll} u_t - \\Delta u \\pm g(u) &= \\mu \\quad &\\text{in } Q_T:=\\Omega \\times (0,T) \\\\ \\phantom{------,} u&=0 &\\text{on } \\partial \\Omega \\times (0,T)\\\\ \\phantom{----,} u(.,0) &=\\omega &\\text{in } \\Omega. \\end{array} \\right. \\end{equation} where $\\mu$ and $\\omega$ are bounded Radon measures in $Q_T$ and $\\Omega$ respectively and $g(u) \\sim e^{a |u|^q} $ with $a>0$ and $q \\geq 1$. We provide a sufficient condition in terms of fractional maximal potentials of $\\mu$ and $\\omega"},"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":"1312.2509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-09T16:47:18Z","cross_cats_sorted":[],"title_canon_sha256":"c894132e8649a49392c02fa41e4f0771a6451899888410cd1a600eed831ab7f2","abstract_canon_sha256":"a1a98127ac0584b2f165dff359c88130479a3b6d0e1ba36778fb973147600774"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:10.131257Z","signature_b64":"2O5+4O9XdUOuAIAWr5a2gcneBqXR4WAGxopoacVUnN2dsQPKyJyPunVxr6y6b8Usvqea64NDFH1rXVoPmxCqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fd82e0965e777c5d9cfe0252f52b80b2530560366aa2a2c028f071dbfd18547","last_reissued_at":"2026-05-18T03:05:10.130710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:10.130710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic equations with exponential nonlinearity and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Phuoc-Tai Nguyen","submitted_at":"2013-12-09T16:47:18Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in ${\\mathbb R}^N$ and $T>0$. We study the problem \\begin{equation} (P)\\left\\{ \\begin{array}{lll} u_t - \\Delta u \\pm g(u) &= \\mu \\quad &\\text{in } Q_T:=\\Omega \\times (0,T) \\\\ \\phantom{------,} u&=0 &\\text{on } \\partial \\Omega \\times (0,T)\\\\ \\phantom{----,} u(.,0) &=\\omega &\\text{in } \\Omega. \\end{array} \\right. \\end{equation} where $\\mu$ and $\\omega$ are bounded Radon measures in $Q_T$ and $\\Omega$ respectively and $g(u) \\sim e^{a |u|^q} $ with $a>0$ and $q \\geq 1$. 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