Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation
| dc.contributor.author | Bouzelmate, Arij | |
| dc.contributor.author | Gmira, Abdelilah | |
| dc.contributor.author | Reyes, Guillermo | |
| dc.date.accessioned | 2021-08-06T19:11:23Z | |
| dc.date.available | 2021-08-06T19:11:23Z | |
| dc.date.issued | 2007-05-09 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14229 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | p-Laplacian | |
| dc.subject | Ornstein-Uhlenbeck diffusion equations | |
| dc.subject | Self-similar solutions | |
| dc.subject | Shooting technique | |
| dc.title | Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation | |
| dc.type | Article |