Spain. 04.12.2020. Our team member Jon Asier Bárcena Petisco and our Head Enrique Zuazua made a contribution to the DyCon Blog about “Averaged dynamics and control for heat equations with random diffusion“:
We want to determine if, given a positive random variable α and an initial configuration
y^0 \in L^2(G), there is some f \in L^2((0,T) \times G_0) such that ~y (T,⋅)= 0.
In order to illustrate the effect of averaging in the dynamics, let us study the dynamics of (1) when
G = R^d and f=0. As averaging and the Fourier transform commute, we work on the Fourier transform of the fundamental solution of the heat equation, which is given by exp(− \alpha |ξ|^2 t).
Take a look the detailed explanation at DyCon Blog