{"paper":{"title":"Nonhomogeneous Boundary-Value Problems for One-Dimensional Nonlinear Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bing-Yu Zhang, Jerry L. Bona, Shu-Ming Sun","submitted_at":"2015-02-28T04:37:44Z","abstract_excerpt":"This paper is concerned with initial-boundary-value problems (IBVPs) for a class of nonlinear Schr\\\"odinger equations posed either on a half line $\\mathbb{R}^+$ or on a bounded interval $(0, L)$ with nonhomogeneous boundary conditions. For any $s$ with $0\\leq s < 5/2$ and $s \\not = 3/2$, it is shown that the relevant IBVPs are locally well-posed if the initial data lie in the $L^2$--based Sobolev spaces $H^s(\\mathbb{R}^+) $ in the case of the half line and in $H^s (0, L)$ on a bounded interval, provided the boundary data are selected from $H^{(2s+1)/4}_{loc} (\\mathbb{R}^+)$ and $H^{(s+ 1) /2}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00065","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"}