{"paper":{"title":"Asymptotic parabolicity for strongly damped wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genni Fragnelli, Gis\\`ele Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli","submitted_at":"2013-01-21T20:47:13Z","abstract_excerpt":"For $S$ a positive selfadjoint operator on a Hilbert space, \\[ \\frac{d^2u}{dt}(t) + 2 F(S)\\frac{du}{dt}(t) + S^2u(t)=0 \\] describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function. Under suitable hypotheses, it is shown that \\[ u(t)=v(t)+ w(t) \\] where $v$ satisfies \\[ 2F(S)\\frac{dv}{dt}(t)+ S^2v(t)=0 \\] and \\[ \\frac{w(t)}{\\|v(t)\\|} \\rightarrow 0, \\; \\text{as} \\; t \\rightarrow +\\infty. \\] The required initial condition $v(0)$ is given in a canonical way in terms of $u(0)$, $u'(0)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4979","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"}