{"paper":{"title":"Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christos Xenophontos, Jens Markus Melenk, Lisa Oberbroeckling","submitted_at":"2011-08-09T18:27:45Z","abstract_excerpt":"We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \\epsilon \\le \\mu \\le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes the solution(s) to have \\emph{boundary layers} which overlap and interact, based on the relative size of $\\epsilon$ and $% \\mu$. We construct full asymptotic expansions together with error bounds that cover the complete range $0 < \\epsilon \\leq \\mu \\leq 1$. For the present case of analytic input data, we derive derivative growth estimates for the terms of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2002","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"}