|
|||||
|
|
On the Nature of Ill-Posedness of the Forward-Backward Heat Equation |
|
| Authors: | Marina Chugunova Illya M Karabash Sergei G Pyatkov |
| Institution: | 1. University of Toronto, 40 St. George Str., Toronto, Ontario, M5S 2E4, Canada 2. Department of Math and Stat, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada 3. Institute of Applied Mathematics and Mechanics, R. Luxemburg str. 74, Donetsk, 83114, Ukraine 4. Department of Math., University of Hanty-Mansiisk, Chekhov st. 16, 628012, Hanty-Mansiisk, Russia |
| Abstract: | We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by a J-self-adjoint linear operator L depending on a small parameter. The problem originates from the lubrication approximation of a viscous fluid film on the inner surface of a rotating cylinder. For a certain range of the parameter we rigorously prove the conjecture, based on numerical evidence, that the complete set of eigenvectors of the operator L does not form a Riesz basis in L2(-p, p)\mathcal{L}^2(-\pi, \pi). Our method can be applied to a wide range of evolution problems given by PT-symmetric operators. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |