{"paper":{"title":"On existence and uniqueness of solutions for semilinear fractional wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahiro Yamamoto, Yavar Kian","submitted_at":"2015-10-12T22:52:08Z","abstract_excerpt":"Let $\\Omega$ be a $\\mathcal C^2$-bounded domain of $\\mathbb R^d$, $d=2,3$, and fix $Q=(0,T)\\times\\Omega$ with $T\\in(0,+\\infty]$. In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation $\\partial_t^\\alpha u+\\mathcal A u=f_b(u)$ in $Q$ where $1<\\alpha<2$, $\\partial_t^\\alpha$ corresponds to the Caputo fractional derivative of order $\\alpha$, $\\mathcal A$ is an elliptic operator and the nonlinearity $f_b\\in \\mathcal C^1( \\mathbb R)$ satisfies $f_b(0)=0$ and $|f_b'(u)|\\leq C|u|^{b-1}$ for some $b>1$. We first provide a defini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03478","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"}