Resumen de Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups

Davar Khoshnevisan, Kunwoo Kim

• Consider the stochastic heat equation ∂tu=Lu+λσ(u)ξ, where L denotes the generator of a Lévy process on a locally compact Hausdorff Abelian group G, σ:R→R is Lipschitz continuous, λ≫1 is a large parameter, and ξ denotes space–time white noise on R+×G.

  The main result of this paper contains a near-dichotomy for the (expected squared) energy E(∥ut∥2L2(G)) of the solution. Roughly speaking, that dichotomy says that, in all known cases where u is intermittent, the energy of the solution behaves generically as exp{const⋅λ2} when G is discrete and ≥exp{const⋅λ4} when G is connected.