{"paper":{"title":"On coupled systems of PDEs with unbounded coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2018-10-09T16:04:26Z","abstract_excerpt":"We study the Cauchy problem associated to parabolic systems of the form $D_t\\boldsymbol{u}=\\boldsymbol{\\mathcal A}(t)\\boldsymbol u$ in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$, the space of continuous and bounded functions $\\boldsymbol{f}:\\mathbb{R}^d\\to\\mathbb{R}^m$. Here $\\boldsymbol{\\mathcal A}(t)$ is a weakly coupled elliptic operator acting on vector-valued functions, having diffusion and drift coefficients which change from equation to equation. We prove existence and uniqueness of the evolution operator $\\boldsymbol{G}(t,s)$ which governs the problem in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$ proving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04097","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"}