{"paper":{"title":"Non-linear noise excitation and intermittency under high disorder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Kunwoo Kim","submitted_at":"2013-02-07T00:26:16Z","abstract_excerpt":"Consider the semilinear heat equation $\\partial_t u = \\partial^2_x u + \\lambda\\sigma(u)\\xi$ on the interval $[0\\,,1]$ with Dirichlet zero boundary condition and a nice non-random initial function, where the forcing $\\xi$ is space-time white noise and $\\lambda>0$ denotes the level of the noise. We show that, when the solution is intermittent [that is, when $\\inf_z|\\sigma(z)/z|>0$], the expected $L^2$-energy of the solution grows at least as $\\exp\\{c\\lambda^2\\}$ and at most as $\\exp\\{c\\lambda^4\\}$ as $\\lambda\\to\\infty$. In the case that the Dirichlet boundary condition is replaced by a Neumann b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1621","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"}