{"paper":{"title":"Mixing in Reaction-Diffusion Systems: Large Phase Offsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bjorn Sandstede, Sameer Iyer","submitted_at":"2016-10-20T18:22:28Z","abstract_excerpt":"We consider Reaction-Diffusion systems on $\\mathbb{R}$, and prove diffusive mixing of asymptotic states $u_0(kx - \\phi_{\\pm}, k)$, where $u_0$ is a periodic wave. Our analysis is the first to treat arbitrarily large phase-offsets $\\phi_d = \\phi_{+}- \\phi_{-}$, so long as this offset proceeds in a sufficiently regular manner. The offset $\\phi_d$ completely determines the size of the asymptotic profiles, placing our analysis in the large data setting. In addition, the present result is a global stability result, in the sense that the class of initial data considered are not near the asymptotic p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06527","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"}