Normal deviations from the averaged motion for some reaction-diffusion equations with fast oscillating perturbation (Q1029163)

The normalized difference between the solution \(u_\varepsilon\) of a reaction-diffusion equation in a bounded interval \([0,L]\) perturbed by a fast oscillating term and the solution \(\hat u\) of the corresponding averaged equation is studied. The authors prove that under smoothness assumption for the reaction coefficient a central limit type result holds in \(C([0;T],L^2(0,L))\). The weak limit is identified as the gaussian solution of a linear equation. In order to prove the weak convergence the authors study first the tightness and then they show that the weak limit of any subsequence has independent increment, continuous trajectories, zero mean and a determined covariance.