{"paper":{"title":"On the norm-continuity for evolution family arising from non-autonomous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"EL-Mennaoui Omar, Hafida Laasri","submitted_at":"2018-07-09T12:02:27Z","abstract_excerpt":"We consider evolution equations of the form \\begin{equation*}\\label{Abstract equation} \\dot u(t)+ A(t)u(t)=0,\\ \\ t\\in[0,T],\\ \\ u(0)=u_0, \\end{equation*} where $A(t),\\ t\\in [0,T],$ are associated with a non-autonomous sesquilinear form $\\mathfrak a(t,\\cdot,\\cdot)$ on a Hilbert space $H$ with constant domain $V\\subset H.$ In this note we continue the study of fundamental operator theoretical properties of the solutions. We give a sufficient condition for norm-continuity of evolution families on each spaces $V, H$ and on the dual space $V'$ of $V.$ The abstract results are applied to a class of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03061","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"}