{"paper":{"title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Palmieri, Vladimir Georgiev","submitted_at":"2019-08-08T09:47:43Z","abstract_excerpt":"In this paper, we consider the Cauchy problem for the semilinear damped wave equation on the Heisenberg group with power nonlinearity. We prove that the critical exponent is the Fujita exponent $p_{\\mathrm{Fuj}}(\\mathscr{Q}) = 1+2 / \\mathscr{Q}$, where $\\mathscr{Q}$ is the homogeneous dimension of the Heisenberg group. On the one hand, we will prove the global existence of small data solutions for $p >p_{\\mathrm{Fuj}}(\\mathscr{Q})$ in an exponential weighted energy space. On the other hand, a blow-up result for $1 < p \\leq p_{\\mathrm{Fuj}}(\\mathscr{Q})$ under certain integral sign assumptions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02989","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02989/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}