Resumen de Rate of approach to a singular steady state in quasilinear reaction-diffusion equations

James W. Dold, V. A. Galaktionov , Andrew A. Lacey, Juan Luis Vázquez

• We study the asymptotic behaviour of global-in-time sQlutions to a quasilinear reaction-diffusion equation in the case when it admits a unique stable stationary solution which is not a bounded function (a singular steady state). We investigate the convergence from below of global solutions to the singular state and discover that such a stabilization is not of a self-similar nature. Actually, it is given by a certain matching of different asymptotic developments in the large outer region closer to the boundary and the thin inner region near the singularity.