{"paper":{"title":"Forward-Backward Evolution Equations and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiongmin Yong","submitted_at":"2015-08-14T15:40:32Z","abstract_excerpt":"Well-posedness is studied for a special system of two-point boundary value problem for evolution equations which is called a forward-backward evolution equation (FBEE, for short). Two approaches are introduced: A decoupling method with some brief discussions, and a method of continuation with some substantial discussions. For the latter, we have introduced Lyapunov operators for FBEEs, whose existence leads to some uniform a priori estimates for the mild solutions of FBEEs, which will be sufficient for the well-posedness. For some special cases, Lyapunov operators are constructed. Also, from s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03550","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"}