{"paper":{"title":"Boundary Feedback Control of Complex Ginzburg-Landau Equation with A Simultaneously Space and Time Dependent Coefficient","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Junji Jia","submitted_at":"2006-10-07T21:59:39Z","abstract_excerpt":"Linearized complex Ginzburg-Landau equation models various physical phenomena and the stability controls of them are important. In this paper, we study the control of the LCGLE with a simultaneously space and time dependent coefficient by transforming it into a complex heat equation. It is shown that under certain conditions on the coefficient functions $a_2(\\tilde{x},\\tilde{t})$, the exponential stability of the system at any rate can be achieved by boundary control based on the state feedback. The kernels are {\\it explicitly} calculated as series of approximation and shown to be twice differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610254","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0610254/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}