{"paper":{"title":"First-order linear evolution equations with c\\`adl\\`ag-in-time solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Ricardo Carrizo Vergara","submitted_at":"2019-06-10T17:35:23Z","abstract_excerpt":"In this work we study first-order linear parabolic evolution PDEs over $\\mathbb{R}^{d}\\times\\mathbb{R}$ and $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its spatial Fourier transform is a slow-growing measure over $\\mathbb{R}^{d}\\times\\mathbb{R}$. When the source term is required to has its support on $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, it is shown that there exists a unique solution such that its spatial Fourier transform is a slow-growing measure with support in $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, which i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04145","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"}