The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

摘要

In this paper, we provide supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations ut−Δum=a(x,t)up with m > 0, p > 0. By using a new method to deal with the “blow up sequence”, we obtain the L∞ estimate with optimal exponent 11,pm≥1+2mN. In addition, we also give quite complete results about the existence of periodic solutions for the fast diffusion case 0 < m < 1. As far as we know, there are no results about the fast diffusion case before present work.