{"paper":{"title":"Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity smaller than one","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, Marco Bonacini","submitted_at":"2017-04-28T12:45:26Z","abstract_excerpt":"We prove the existence of a one-parameter family of self-similar solutions with time-dependent tails for Smoluchowski's coagulation equation, for a class of rate kernels $K(x,y)$ which are homogeneous of degree $\\gamma\\in(-\\infty,1)$ and satisfy $K(x,1)\\sim x^{-a}$ as $x\\to 0$, for $a=1-\\gamma$. In particular, for small values of a parameter $\\rho>0$ we establish the existence of a positive self-similar solution with finite mass and asymptotics $A(t)x^{-(2+\\rho)}$ as $x\\to\\infty$, with $A(t)\\sim\\rho t^\\frac{\\rho}{1-\\gamma}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08905","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"}