Periodic behavior for a degenerate fast diffusion equation

This work deals with the study of periodic solutions to a degenerate fast diffusion equation. The existence of the periodic solution to an intermediate problem restraint to a period T is proved first and then the result is extended by the data periodicity to all time real space. The approach involves an appropriate approximating problem whose periodic solution is proved via a fixed point theorem. Next, a passing to the limit procedure leads to the existence of the solution to the original problem on a time period. Finally, the behavior at large time of the solution to a Cauchy problem with periodic data is characterized.