Gamma-convergence of integral functionals depending on vector-valued functions over parabolic domains

De Giorgi conjectured in 1979 that if a sequence of parabolic functionals Gamma converges to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. This paper studies the Gamma convergence for a kind of parabolic functionals, and it supports the De Giorgi’s conjecture.