{"paper":{"title":"Mild solutions are weak solutions in a class of (non)linear measure-valued evolution equations on a bounded domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joep H.M. Evers","submitted_at":"2016-06-04T06:08:56Z","abstract_excerpt":"We study the connection between mild and weak solutions for a class of measure-valued evolution equations on the bounded domain $[0,1]$. Mass moves, driven by a velocity field that is either a function of the spatial variable only, $v=v(x)$, or depends on the solution $\\mu$ itself: $v=v[\\mu](x)$. The flow is stopped at the boundaries of $[0,1]$, while mass is gated away by a certain right-hand side. In previous works [J. Differential Equations, 259 (2015), pp. 1068-1097] and [SIAM J. Math. Anal., 48 (2016), pp. 1929-1953], we showed the existence and uniqueness of appropriately defined mild so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01332","kind":"arxiv","version":2},"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"}