{"paper":{"title":"On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Alberto Lastra, Stephane Malek","submitted_at":"2015-01-16T11:17:51Z","abstract_excerpt":"We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter $\\epsilon$ whose coefficients depend holomorphically on $(\\epsilon,t)$ near the origin in $\\mathbb{C}^{2}$ and are bounded holomorphic on some horizontal strip in $\\mathbb{C}$ w.r.t the space variable. We consider a family of forcing terms that are holomorphic on a common sector in time $t$ and on sectors w.r.t the parameter $\\epsilon$ whose union form a covering of some neighborhood of 0 in $\\mathbb{C}^{\\ast}$, which are asked to share a common formal power series asymptotic expansion of some Gev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03951","kind":"arxiv","version":1},"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"}