{"paper":{"title":"Runge-Kutta time semidiscretizations of semilinear PDEs with non-smooth data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chris Evans, Claudia Wulff","submitted_at":"2015-10-21T13:32:49Z","abstract_excerpt":"We study semilinear evolution equations $ \\frac {{\\rm d} U}{{\\rm d} t}=AU+B(U)$ posed on a Hilbert space ${\\cal Y}$, where $A$ is normal and generates a strongly continuous semigroup, $B$ is a smooth nonlinearity from ${\\cal Y}_\\ell = D(A^\\ell)$ to itself, and $\\ell \\in I \\subseteq [0,L]$, $L \\geq 0$, $0,L \\in I$. In particular the one-dimensional semilinear wave equation and nonlinear Schr$\\\"o$dinger equation with periodic, Neumann and Dirichlet boundary conditions fit into this framework. We discretize the evolution equation with an A-stable Runge-Kutta method in time, retaining continuous s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06246","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"}