{"paper":{"title":"Global nonexistence of solutions for the viscoelastic wave equation of Kirchhoff type with high energy","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gang Li, Linghui Hong, Wenjun Liu","submitted_at":"2011-09-27T14:49:34Z","abstract_excerpt":"In this paper we consider the viscoelastic wave equation of Kirchhoff type:\n$$ u_{tt}-M(\\|\\nabla u\\|_{2}^{2})\\Delta u+\\int_{0}^{t}g(t-s)\\Delta u(s){\\rm d}s+u_{t}=|u|^{p-1}u $$\nwith Dirichlet boundary conditions. Under some suitable assumptions on $g$ and the initial data, we established a global nonexistence result for certain solutions with arbitrarily high energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5916","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"}