DyCon blog: Averaged dynamics and control for heat equations with random diffusion

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