{"paper":{"title":"Asymptotic profiles of solutions for structural damped wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Takeda, Ryo Ikehata","submitted_at":"2016-07-06T23:42:55Z","abstract_excerpt":"In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\\partial_{t}^{2} u - \\Delta u + \\nu (-\\Delta)^{\\sigma} \\partial_{t} u=0$, where $\\nu >0$ and $0< \\sigma \\le1$. Our result is the approximation formula of the solution by a constant multiple of a special function as $t \\to \\infty$, which states that the asymptotic profiles of the solutions are classified into $5$ patterns depending on the values $\\nu$ and $\\sigma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01839","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":""},"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"}