{"paper":{"title":"Averaging approximation to singularly perturbed nonlinear stochastic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"A. J. Roberts, Yan Lv","submitted_at":"2011-07-21T07:15:14Z","abstract_excerpt":"An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \\nu u_{tt}+u_t=\\D u+f(u)+\\nu^\\alpha\\dot{W} on an open bounded domain $D\\subset\\R^n$\\,, $1\\leq n\\leq 3$\\,. Here $\\nu>0$ is a small parameter characterising the singular perturbation, and $\\nu^\\alpha$\\,, $0\\leq \\alpha\\leq 1/2$\\,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $\\nu$, u_t=\\D u+f(u)+\\nu^\\alpha\\dot{W} to an error of $\\ord{\\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4184","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"}