On the nature of the instability of radial power equilibria of a semilinear parabolic equation


The semilinear problem (Formula presented) has positive equilibria of the form u(x, t) = C |x|−a for many values of (N, p). Of concern is getting more information on exactly how stable or unstable these solutions are. When m = 1, the results have a qualitatively different nature for the two cases N ≤ 10 and N ≥ 11.

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Springer INdAM Series