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Linear-reaction time change for quadratic nonlinear diffusion

The substitution

C (x, t) = e^{a t} G (x, τ (t)), τ (t) = {(e^{a t} - 1) / a, t, a \neq = 0, a = 0,

reduces

C_{t} = k \nabla \cdot (C \nabla C) + a C

to

G_{τ} = k \nabla \cdot (G \nabla G)

.

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