{"paper":{"title":"Well-posedness results for a class of semi-linear super-diffusive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ciprian Gal, Edgardo Alvarez, Mahamadi Warma, Valentin Keyantuo","submitted_at":"2018-08-07T15:59:14Z","abstract_excerpt":"In this paper we investigate the following fractional order in time Cauchy problem \\begin{equation*} \\begin{cases} \\mathbb{D}_{t}^{\\alpha }u(t)+Au(t)=f(u(t)), & 1<\\alpha <2, u(0)=u_{0},\\,\\,\\,u^{\\prime }(0)=u_{1}. & \\end{cases}% \\end{equation*}% The fractional in time derivative is taken in the classical Caputo sense. In the scientific literature such equations are sometimes dubbed as fractional-in time wave equations or super-diffusive equations. We obtain results on existence and regularity of local and global weak solutions assuming that $A$ is a nonnegative self-adjoint operator with compac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02434","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"}