{"paper":{"title":"Singular asymptotic expansion of the exact control for a linear model of the Rayleigh beam","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Arnaud Munch, Carlos Castro","submitted_at":"2019-07-09T12:47:08Z","abstract_excerpt":"The Petrowsky type equation $y_{tt}^\\eps+\\eps y_{xxxx}^\\eps - y_{xx}^\\eps=0$, $\\eps>0$ encountered in linear beams theory is null controllable through Neumann boundary controls. Due to the boundary layer of size of order $\\sqrt{\\eps}$ occurring at the extremities, these boundary controls get singular as $\\eps$ goes to $0$. Using the matched asymptotic method, we describe the boundary layer of the solution $y^\\eps$ then derive a rigorous second order asymptotic expansion of the control of minimal $L^2-$norm, with respect to the parameter $\\eps$. In particular, we recover that the leading term o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04118","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"}