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We first classify all the positive radial solutions in case $\\Omega$ is a ball, according to their behavior at the boundary. Then we obtain tha"},"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":"1808.00407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-01T16:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"0b54fc137e3615a3b739099a5d19d52b7f480847b688ebbd9ad2fcd22ac0d9dd","abstract_canon_sha256":"08c63ba04140c45cc1b0513ef8ea7910f9c38792b05bff6eac1e1884a1f3ae63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:20.715747Z","signature_b64":"HLH3Fgx5SnWf994V6HtjbgIMYLlhHD1xeoeBaYQpW+lljQEnVbaTL62K1q9aVQs8IKE85nKclv7oSoxYaQJPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82a447f2cd90cf2ba6c373f2711a30d607280edcca1d1bbed754024819e8a508","last_reissued_at":"2026-05-17T23:47:20.715182Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:20.715182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global and blow-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gurpreet Singh, Jacques Giacomoni, Marius Ghergu","submitted_at":"2018-08-01T16:30:28Z","abstract_excerpt":"We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form $$ \\left\\{ \\begin{aligned} \\Delta_{p} u&=v^{m}|\\nabla u|^{\\alpha}&&\\quad\\mbox{ in }\\Omega,\\\\ \\Delta_{p} v&=v^{\\beta}|\\nabla u|^{q} &&\\quad\\mbox{ in }\\Omega, \\end{aligned} \\right. $$ where $\\Omega\\subset\\R^N$ $(N\\geq 2)$ is either a ball or the whole space, $1<p<\\infty$, $m, q>0$, $\\alpha\\geq 0$, $0\\leq \\beta\\leq m$ and $(p-1-\\alpha)(p-1-\\beta)-qm\\neq 0$. We first classify all the positive radial solutions in case $\\Omega$ is a ball, according to their behavior at the boundary. 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