{"paper":{"title":"Stochastic stability of master-slave synchronization for dissipative PDEs with Burgers-type nonlinearity and application to data assimilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"In\\'es P. Mari\\~no, Joaqu\\'in Miguez","submitted_at":"2026-07-18T23:33:01Z","abstract_excerpt":"We investigate the stochastic stability of master--slave synchronization for a class of nonlinear dissipative evolution equations with a Burgers-type convective nonlinearity and a polynomial linear differential operator. The family includes the Burgers, Kuramoto--Sivashinsky, Kawahara, Benney--Lin, and Nikolaevskiy equations. Under periodic boundary conditions, each equation is represented through a finite-dimensional Fourier truncation, yielding a complex state vector coupled to a slave system driven by observations of the master. We first establish local exponential stability of the determin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17002","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/2607.17002/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"}