{"paper":{"title":"Local and global existence of solutions to a strongly damped wave equation of the $p$-Laplacian type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohammad A. Rammaha, Nicholas J. Kass","submitted_at":"2017-05-18T17:08:47Z","abstract_excerpt":"This article focuses on a quasilinear wave equation of $p$-Laplacian type: $$ u_{tt} - \\Delta_p u - \\Delta u_t=0$$ in a bounded domain $\\Omega\\subset\\mathbb{R}^3$ with a sufficiently smooth boundary $\\Gamma=\\partial\\Omega$ subject to a generalized Robin boundary condition featuring boundary damping and a nonlinear source term. The operator $\\Delta_p$, $2 < p < 3$, denotes the classical $p$-Laplacian. The nonlinear boundary term $f (u)$ is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from $W^{1,p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06696","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"}