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The origin of non self-similar blow-up in higher-order reaction-diffusion(parabolic), wave (hyperbolic) and nonlinear dispersion equations is explainedby a combination of various methods.  Some links and similarities with double-log blow-up terms occurring inearlier studies of plasma physics second-order parabolic equations and thenonlinear critical Schr\"odinger equation are discussed. On the other hand, thelog-log factor obtained in Petrovskii's boundary regularity study of aparaboloid vertex for the heat equation in 1934 was the first its appearance inPDE theory.

Blow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs