{"paper":{"title":"Regularity properties for evolution family governed by non-autonomous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hafida Laasri","submitted_at":"2017-06-20T09:31:27Z","abstract_excerpt":"This paper gives further regularity properties of the evolution family associated with a non-autonomous evolution equation \\begin{equation*}\\label{Abstract equation} \\dot u(t)+A(t)u(t)=f(t),\\ \\ t\\in[0,T],\\ \\ u(0)=u_0, \\end{equation*} where $A(t),\\ t\\in [0,T],$ arise from non-autonomous sesquilinear forms $\\mathfrak a(t,\\cdot,\\cdot)$ on a Hilbert space $H$ with constant domain $V\\subset H.$ Results on norm continuity, compactness and results on the \\textit{Gibbs} character of the evolution family are established. The abstract results are applied to the Laplacian operator with time dependent Rob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06340","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"}