Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source

摘要

Self-similar blow-up behaviour for the fourth-order quasilinear p-Laplacian equation with source, ut=−(|uxx|nuxx)xx+|u|p−1uin R×R+, where n>0,p>1, is studied. Using variational setting for p=n+1 and branching techniques for p⁄=n+1, finite and countable families of blow-up patterns of the self-similar form uS(x,t)=(T−t)−1p−1f(y),where y=x/(T−t)β,β=−p−(n+1)2(n+2)(p−1), are described by an analytic-numerical approach. Three parameter ranges: p=n+1 (regional), p>n+1 (single point), and 1