{"paper":{"title":"A revised proof of uniqueness of self-similar profiles to Smoluchowski's coagulation equation for kernels close to constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Niethammer, Juan J.L. Vel\\'azquez, Sebastian Throm","submitted_at":"2015-10-12T16:49:01Z","abstract_excerpt":"In this article we correct the proof of a uniqueness result for self-similar solutions to Smoluchowski's coagulation equation for kernels $K=K(x,y)$ that are homogeneous of degree zero and close to constant in the sense that \\begin{equation*}\n  -\\varepsilon \\leq K(x,y)-2 \\leq \\varepsilon \\left( \\Big(\\frac{x}{y}\\Big)^{\\alpha} + \\Big(\\frac{y}{x}\\Big)^{\\alpha}\\right) \\end{equation*} for $\\alpha \\in [0,\\frac 1 2)$. Assuming in addition that $K$ has an analytic extension to $\\mathbb{C}\\setminus(-\\infty,0]$ and prescribing the precise asymptotic behaviour of $K$ at the origin, we prove that self-sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03361","kind":"arxiv","version":3},"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"}