Convergence of Solutions of a Rescaled Evolution Nonlocal Cross-Diffusion Problem to Its Local Diffusion Counterpart

for (t, x) ∈ QT = (0, T ) × Ω, and for some u0 : Ω → R+. Here, R+ = [0,∞), and the diffusion kernel, J : RN → R+, is usually assumed to be continuous, radial, radially non-increasing, and with unitary norm in L1(RN ). Terming the equation (1) as the evolution nonlocal p−Laplacian equation has its reasons. Firstly, because it arises as the gradient descent of the Euler-Lagrange equation of the energy functional Enl p (v) = ∫