Accession Number:
AD0680761
Title:
ON THE PRINCIPLE OF EXCHANGE OF STABILITIES,
Descriptive Note:
Corporate Author:
RAND CORP SANTA MONICA CALIF
Personal Author(s):
Report Date:
1968-12-01
Pagination or Media Count:
57.0
Abstract:
Proof is given of a perturbation theorem A class of real, bounded non-self-ajoint perturbations of norm epsilon to real self-adjoint operators preserves the reality of the simple eigenvalues for epsilon sufficiently small. A bound is obtained on epsilon. Application is made to Benard convection with constant heat sources, radiation, particular time-dependent profiles, variable fluid properties, and nonlinear equations of state, and to instability of circular Couette flow for a range of gap widths. In each case the growth rate is the eigenvalue, and hence if epsilon is less than the critical value, traveling waves--whether growing or decaying-- are forbidden. Author
Descriptors:
Subject Categories:
- Meteorology
- Theoretical Mathematics
- Fluid Mechanics