Shrinking self-similar solutions of a nonlinear diffusion equation with nondivergence form ✩

In this paper we study the shrinking self-similar solutions of the nonlinear diffusion equation with nondivergence form ∂u ∂t = umΔu (m 1). This kind of solutions possess the properties of finite speed propagation of perturbations and their supports are shrinking. We establish the existence and uniqueness for this kind of solutions. In addition, we study some properties of the shrinking self-similar solutions.  2003 Elsevier Inc. All rights reserved.