Eulalia Nualart: Asymptotics for some non-linear stochastic heat equations

Abstract: Consider the following stochastic heat equation,
∂ut(x)/∂t = −ν(−Δ)α/2ut(x)+σ(ut(x))F˙(t,x),t[is greater than]0,x∈ℝd.

Here −ν(−Δ)α/2 is the fractional Laplacian with ν[is greater than]0 and α∈(0,2], σ:ℝ→ℝ is a globally Lipschitz function, and F˙(t,x) is a Gaussian noise which is white in time and colored in space. Under some suitable conditions, we will explore the effect of the initial data on the spatial asymptotic properties of the solution. We also prove a strong comparison principle thus filling an important gap in the literature.
Joint work with Mohammud Foondun (University of Strathclyde).

Recording during the meeting "Stochastic Partial Differential Equations" the May 16, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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