{"paper":{"title":"On the continuous dependence on the coefficients of evolutionary equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Marcus Waurick","submitted_at":"2016-06-24T15:51:51Z","abstract_excerpt":"In an abstract Hilbert space setting, we discuss many linear phenomena of mathematical physics. The functional analytic framework presented is used to address continuous dependence of the solution operators $\\mathcal{S}(\\mathcal{M})$ of certain (linear partial differential) equations on the coefficients $\\mathcal{M}$. For this, we introduce a particular class of coefficients $\\mathcal{M}$ and study the (nonlinear) mapping $\\mathcal{M}\\mapsto \\mathcal{S}(\\mathcal{M})$. We provide criteria that guarantee the continuity of $\\mathcal{S}(\\cdot)$ under the norm, the strong, and the weak operator top"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07731","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"}