{"paper":{"title":"Regularity, asymptotic behavior and partial uniqueness for Smoluchowski's coagulation equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jos\\'e Alfredo Ca\\~nizo, St\\'ephane Mischler","submitted_at":"2008-03-10T17:45:51Z","abstract_excerpt":"We consider Smoluchowski's equation with a homogeneous kernel of the form $a(x,y) = x^\\alpha y ^\\beta + x^\\beta y^\\alpha$ with $-1 < \\alpha \\leq \\beta < 1$ and $\\lambda := \\alpha + \\beta \\in (-1,1)$. We first show that self-similar solutions of this equation are infinitely differentiable and prove sharp results on the behavior of self-similar profiles at $y = 0$ in the case $\\alpha < 0$. We also give some partial uniqueness results for self-similar profiles: in the case $\\alpha = 0$ we prove that two profiles with the same mass and moment of order $\\lambda$ are necessarily equal, while in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1462","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"}