Asymptotically self-similar global solutions of a general semilinear heat equation

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Well-posedness, global existence and large time behavior for Hardy–Hénon parabolic equations (2017, methodology): “We use similar argument as in [12].”
The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces (2002, methodology): “The timet maps of the semiflow generated by these solutions satisfy various continuity properties, which can be proved by modifications to the contraction mapping argument, as is done for example in [29,47,48,54].”