{"paper":{"title":"Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e A. Ca\\~nizo, Mar\\'ia J. C\\'aceres, St\\'ephane Mischler","submitted_at":"2010-10-26T17:02:09Z","abstract_excerpt":"We study the asymptotic behavior of linear evolution equations of the type \\partial_t g = Dg + Lg - \\lambda g, where L is the fragmentation operator, D is a differential operator, and {\\lambda} is the largest eigenvalue of the operator Dg + Lg. In the case Dg = -\\partial_x g, this equation is a rescaling of the growth-fragmentation equation, a model for cellular growth; in the case Dg = -x \\partial_x g, it is known that {\\lambda} = 2 and the equation is the self-similar fragmentation equation, closely related to the self-similar behavior of solutions of the fragmentation equation \\partial_t f "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5461","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"}