{"paper":{"title":"Non-homogeneous Problems for Nonlinear Schr\\\"odinger Equations in a Strip Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shu-Ming Sun, Yu Ran","submitted_at":"2017-02-09T09:25:02Z","abstract_excerpt":"This paper studies the initial-boundary-value problem (IBVP) of a nonlinear Schr\\\"odinger equation posed on a strip domain $\\mathbb{R}\\times[0,1]$ with non-homogeneous Dirichlet boundary conditions. For any $s\\ge0$, if the initial data $\\varphi(x,y)$ is in Sobolev space $H^s(\\mathbb{R}\\times[0,1])$ and the boundary data $h(x,t)$ is in $$ {\\cal H}^s (\\mathbb{R} ) = \\left \\{ h (x, t) \\in L^2 ( \\mathbb{R}^2 ) \\ \\big | \\ ( 1 + |\\lambda | + |\\xi|)^{\\frac12} ( 1+ |\\lambda | + |\\xi |^2 )^{\\frac{s}{2}}\\hat h ( \\lambda, \\xi ) \\in L^2 (\\mathbb{R}^2 ) \\right \\} $$ where $\\hat h $ is the Fourier transform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02756","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"}