Decay and growth for a nonlinear parabolic difference equation

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation u t = Δ u + μ | ∇ u | uₜ=Δ u+μ |∇ u| when μ > 0 , μ >0, and a new growth result when μ > 0 μ >0 .