{"paper":{"title":"On parametric Gevrey asymptotics for 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, St\\'ephane Malek","submitted_at":"2014-03-10T19:15:13Z","abstract_excerpt":"We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter $\\epsilon$ with vanishing initial data at complex time $t=0$ and whose coefficients depend analytically 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. This problem is assumed to be non-Kowalevskian in time $t$, therefore analytic solutions at $t=0$ cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2350","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"}