Abstract

We study the self-similar solutions of the equation u_t − div(|∇u|^p−2∇u) = 0 in R^N, where N ≥ 1, p in (1,2). We provide a complete description of the signed solutions of the form u(x,t) = (±t)^{−α ∕ β}w((±t)^{−1 ∕ β}|x|), regular or singular at x = 0, with α,β real, β≠0, and possibly not defined on all of R^N × (0,±∞).

Keywords

degenerate parabolic equations, self-similar solutions

Mathematical Subject Classification

Primary: 35K65

Secondary: 34C35

Authors