{"paper":{"title":"Invariance of Convex Sets for Non-autonomous Evolution Equations Governed by Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Dominik Dier, El Maati Ouhabaz (IMB), Wolfgang Arendt","submitted_at":"2013-03-05T20:34:25Z","abstract_excerpt":"We consider a non-autonomous form $\\fra:[0,T]\\times V\\times V \\to \\C$ where $V$ is a Hilbert space which is densely and continuously embedded in another Hilbert space $H$. Denote by $\\A(t) \\in \\L(V,V')$ the associated operator. Given $f \\in L^2(0,T, V')$, one knows that for each $u_0 \\in H$ there is a unique solution $u\\in H^1(0,T;V')\\cap L^2(0,T;V)$ of $$\\dot u(t) + \\A(t) u(t) = f(t), \\, \\, u(0) = u_0.$$ %\\begin{align*} %&\\dot u(t) + \\A(t)u(t)= f(t)\\ %& u(0)=u_0. %\\end{align*} This result by J. L. Lions is well-known. The aim of this article is to find a criterion for the invariance of a clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1167","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"}