Refined asymptotic expansions for nonlocal diffusion equations

Abstract. We study the asymptotic behavior for solutions to nonlocal diffusion models of the form ut = J ∗ u − u in the whole Rd with an initial condition u(x, 0) = u0(x). Under suitable hy-potheses on J (involving its Fourier transform) and u0, it is proved an expansion of the form∥∥∥u(u) − ∑ |α|≤k (−1)|α| α! u0(x)xα d