Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents

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Optimal Liouville theorems for superlinear parabolic problems (2020, background): “Theorem 26.6 and Remark 26.7]. Let us also mention that (18) fails if, for example, Ω is a ball, T = ∞ and f(u) = up with p = pS: Then there exist global solutions such that limt→∞ ku(·,t)k∞ = ∞ (see [13] for the precise asymptotic behavior of such solutions and notice that that behavior again stron”
Green's function and infinite-time bubbling in the critical nonlinear heat equation (2016, background): “Galaktionov and King discovered in [14] that this radial blow-up solution does have a bubbling asymptotic profile as t→ +∞ of the form uα∗(r, t) ≈ αn ( μ(t) μ(t)2 + r2 ) n−2 2 , r = |x|.”