Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation
Date
2007-05-09
Authors
Bouzelmate, Arij
Gmira, Abdelilah
Reyes, Guillermo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
This paper concerns the existence, uniqueness and asymptotic properties (as r = |x| → ∞) of radial self-similar solutions to the nonlinear Ornstein-Uhlenbeck equation
vt = Δpv + x · ∇(|v|q-1v)
in ℝN x (0, +∞). Here q > p - 1 > 1, N ≥ 1, and Δp denotes the p-Laplacian operator. These solutions are of the form
v(x, t) = t−γU(cxt-σ),
where γ and σ are fixed powers given by the invariance properties of differential equation, while U is a radial function, U(y) = u(r), r = |y|. With the choice c = (q - 1)-1/p, the radial profile u satisfies the nonlinear ordinary differential equation.
Description
Keywords
p-Laplacian, Ornstein-Uhlenbeck diffusion equations, Self-similar solutions, Shooting technique
Citation
Bouzelmate, A., Gmira, A., & Reyes, G. (2007). Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation. <i>Electronic Journal of Differential Equations, 2007</i>(67), pp. 1-21.
Rights
Attribution 4.0 International