{"paper":{"title":"Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohammad A. Rammaha, Sawanya Sakuntasathien, Yanqiu Guo","submitted_at":"2016-07-22T07:16:47Z","abstract_excerpt":"We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source: \\begin{align*} \\begin{cases} u_{tt}- k(0) \\Delta u - \\int_0^{\\infty} k'(s) \\Delta u(t-s) ds + |u_t|^{m-1}u_t=|u|^{p-1}u, \\;\\;\\;\\;\\; \\Omega \\times (0,T), \\\\ u(x,t)=u_0(x,t), \\quad \\text{ in } \\Omega \\times (-\\infty,0], \\end{cases} \\end{align*} where $\\Omega$ is a bounded domain in $\\mathbb R^3$ with a Dirichl\\'et boundary condition. The relaxation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06579","kind":"arxiv","version":2},"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"}