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Non-self-similar dead-core rate for the fast diffusion equation with strong absorption. (English) Zbl 1194.35059
Authors’ abstract: We study the dead-core problem for the fast diffusion equation with strong absorption. Unlike in many other related problems of singularity formation, we show that the temporal rate of formation of the dead-core is not self-similar. We moreover obtain precise estimates on rescaled solutions and on the single-point final dead-core profile. Results of this type were up to now known only for problems with linear diffusion. The proofs rely on self-similar variables and require a delicate use of the Zelenyak method.
##### MSC:
 35B40 Asymptotic behavior of solutions of PDE 35A20 Analytic methods, singularities (PDE) 35K59 Quasilinear parabolic equations 35K57 Reaction-diffusion equations 35K15 Second order parabolic equations, initial value problems