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Remark that $2=1+2/N$ is well-known as the Fujita exponent. If $p>2$, then there exists a small global-in-time solution of the damped wave equation for some initial data small enough (see Ikehata'05), and if $p<2$, then global-in-time solutions cannot exist for any positive initial data (see Ogawa-Takeda'09 and Lai-Yin'17). The result is that for given initial d"},"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":"1711.00994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-03T02:07:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"fd2189a78eccd4e785b7f8fd099ba15f83557398f2e56de9d5631216a8888fd9","abstract_canon_sha256":"5ec7ac957bd809a611d170baa31ae90300a2c6986cc3a41ffe1fd0a497e76c6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:24.328628Z","signature_b64":"7sQtUY6BPvM5zxJe+qvTC6nctd/OKTo9OVU9uAyKEgkw3M2QkIHZg0wMbnhk9q/GvGFlowO4QuSCe17QszKMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fffe168261c3d43db1053ede63c65481e46fc81de64ad6a5f81cf2dd7b3e91f7","last_reissued_at":"2026-05-18T00:31:24.328206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:24.328206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remark on upper bound for lifespan of solutions to semilinear evolution equations in a two-dimensional exterior domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Masahiro Ikeda, Motohiro Sobajima","submitted_at":"2017-11-03T02:07:39Z","abstract_excerpt":"In this paper we consider the initial-boundary value problem for the heat, damped wave, complex-Ginzburg-Landau and Schr\"odinger equations with the power type nonlinearity $|u|^p$ with $p in (1,2]$ in a two-dimensional exterior domain. Remark that $2=1+2/N$ is well-known as the Fujita exponent. If $p>2$, then there exists a small global-in-time solution of the damped wave equation for some initial data small enough (see Ikehata'05), and if $p<2$, then global-in-time solutions cannot exist for any positive initial data (see Ogawa-Takeda'09 and Lai-Yin'17). 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