Stability of a Hot Smoluchowski Fluid
| dc.creator | Streater, R. F. | |
| dc.date | 2001-03-21 | |
| dc.date.accessioned | 2026-07-07T04:28:21Z | |
| dc.date.available | 2026-07-07T04:28:21Z | |
| dc.description | We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on the boundary, with no-escape boundary conditions for the material. For the special case, where the temperature on the boundary is the same at both ends, the linearised equations for small perturbations about a stationary solution are derived; they are subject to the boundary conditions, Dirichlet for the temperature and no-flow conditions for the material. The spectrum of the generator L of time-evolution, regarded as an operator on the Hilbert space of square-integrable functions on [0,1], is shown to be real, discrete and non-positive, even though L is not self-adjoint. This result is necessary for the stability of the stationary state, but might not be sufficient. The problem lies in the fact that L is not a sectorial operator; its numerical range is the whole of the complex plane. | |
| dc.description | 9 pages, to appear in "Open Systems and Information Dynamics", Kluwer | |
| dc.identifier | https://arxiv.org/abs/math-ph/0103026 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0103026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56758 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.title | Stability of a Hot Smoluchowski Fluid | |
| dc.type | text |