The concentration‐compactness principle and the asymptotic behavior for some degenerate parabolic equation

In this paper we study the existence and asymptotic behavior of the global solutions of some degenerate parabolic equation with critical Sobolev exponent. In particular, we apply the concentration‐compactness principle of P.‐L. Lions to the study of the asymptotic behavior of global solutions with the initial value in “stable set”.