Proves that the difference D(t) between the diffusion-wave profile and free-wave evolution is O(t^{1/4}) in 1D but has a logarithmic lower bound in 2D when initial velocity has nonzero mass.
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On the $L^{2}$ estimates of the diffusion waves
Proves that the difference D(t) between the diffusion-wave profile and free-wave evolution is O(t^{1/4}) in 1D but has a logarithmic lower bound in 2D when initial velocity has nonzero mass.