{"paper":{"title":"Stability and error estimates of a general modified quasi-boundary value method via a semi-linear backward parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Vo Anh Khoa","submitted_at":"2015-10-16T11:03:13Z","abstract_excerpt":"Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with locally Lipschitz source: $\\partial_{t}u+\\mu\\left(t\\right)\\mathcal{A}u\\left(t\\right)=f\\left(t,u\\right)$ where $\\mathcal{A}:\\mathcal{D}\\left(\\mathcal{A}\\right)\\subset\\mathcal{H}\\to\\mathcal{H}$ is a positive, self-adjoint and unbounded linear operator on the Hilbert space $\\mathcal{H}$. The problem arises in many applications, but it is in general ill-posed. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04836","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"}