{"paper":{"title":"Global Stabilization of BBM-Burgers' Type Equations by Nonlinear Boundary Feedback Control Laws: Theory and Finite Element Error Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.NA","authors_text":"Amiya Kumar Pani, Sudeep Kundu","submitted_at":"2018-12-05T16:19:56Z","abstract_excerpt":"In this article, global stabilization results for the Benjamin-Bona-Mahony-Burgers' (BBM-B) type equations are obtained using nonlinear Neumann boundary feedback control laws. Based on the $C^0$-conforming finite element method, global stabilization results for the semidiscrete solution are also discussed. Optimal error estimates in $L^\\infty(L^2)$, $L^\\infty(H^1)$ and $L^\\infty(L^\\infty)$-norms for the state variable are derived, which preserve exponential stabilization property. Moreover, for the first time in the literature, superconvergence results for the boundary feedback control laws ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02084","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"}