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We give general conditions for a family $u_p$ of sign-changing stationary solutions of \\eqref{problemAbstract}, under which the solution of \\eqref{problemAbstract} with initial value $v_0="},"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":"1403.0115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-01T18:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"837f0dc34d6790d77a04ef8371fc041b1149d8908faabc1bb7637aacf104a93d","abstract_canon_sha256":"104af7eb4d94baad95f216a2ec43af7f804a5ebb264edefc1ea4fa114b7ecbfb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.951693Z","signature_b64":"U3LUv/e52G+LDAEY+HUlQRQN780KQPfDoKwzQ+JSCA7fXPdZavSOfDqS7k8jEuUQwUD2PLngqzSVZinL7pyZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"960817bd37ebbb936e12194415340d9a4aad944cca085f12bcc9d137b1f048bd","last_reissued_at":"2026-05-18T01:22:48.951193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.951193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow up of solutions of semilinear heat equations in non radial domains of $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca De Marchis, Isabella Ianni","submitted_at":"2014-03-01T18:40:38Z","abstract_excerpt":"We consider the semilinear heat equation \\begin{equation}\\label{problemAbstract}\\left\\{\\begin{array}{ll}v_t-\\Delta v= |v|^{p-1}v & \\mbox{in}\\Omega\\times (0,T)\\\\ v=0 & \\mbox{on}\\partial \\Omega\\times (0,T)\\\\ v(0)=v_0 & \\mbox{in}\\Omega \\end{array}\\right.\\tag{$\\mathcal P_p$} \\end{equation} where $p>1$, $\\Omega$ is a smooth bounded domain of $\\mathbb R^2$, $T\\in (0,+\\infty]$ and $v_0$ belongs to a suitable space. 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