Non-self-similar dead-core rate for the fast diffusion equation with strong absorption
Jong‐Shenq Guo, Chia-Tung Ling, Philippe Souplet · Nonlinearity · 2010
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.