Blow-up and global asymptotics of the limit unstable Cahn-Hilliard equation

We study the asymptotic behavior of classes of global and blow-up solutions of a semilinear parabolic equation of the "limit" Cahn-Hilliard type u(t) = -Delta(Delta u + | u|(p-1)u) in R-N x R+, p> 1, with bounded integrable initial data. We show that in some {p, N}-parameter ranges it admits a countable set of blow-up similarity patterns. The most interesting set of blow-up solutions is constructed at the first critical exponent p = p(0) = 1+2/N N, where the first simplest pro. le is shown to be stable. Unlike the blow-up case, we show that, for p = p(0), the set of global decaying source-type similarity solutions is continuous and determine the stable mass-branch. We prove that there exists a countable spectrum of critical exponents {p = p(l) = 1+ 2/ N+l, l = 0, 1, 2,...} creating bifurcation branches, which play a key role in general description of solutions globally decaying as t--> infinity.