{"paper":{"title":"Boundary layer expansions for initial value problems with two complex time variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Alberto Lastra, St\\'ephane Malek","submitted_at":"2019-04-09T19:55:49Z","abstract_excerpt":"We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter $\\epsilon$. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to $\\epsilon$, in adequate domains. The construction of such analytic solutions is closely related to the procedure of summation with respect to an analytic germ, put forward in[J. Mozo-Fern\\'andez, R. Sch\\\"afke, Asymptotic expansions and summability with respect to an analytic germ, Publ. Math. 63 (2019), no. 1,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04886","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"}