Abstract

We will show that for n = 1, 2, as m → 0 the solution u^(m) of the fast diffusion equation ∂u ∕ ∂t = Δ(u^m ∕ m), u > 0, in Rⁿ × (0,∞), u(x,0) = u₀(x) ≥ 0 in Rⁿ, where u₀ in L¹(Rⁿ) ∩ L^∞(Rⁿ) will converge uniformly on every compact subset of Rⁿ × (0,T) to the maximal solution of the equation v_t = Δlog v, v(x,0) = u₀(x), where T = ∞ for n = 1 and T = ∫ _R²u₀dx ∕ 4π for n = 2.

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