ON THE PRINCIPLE OF EXCHANGE OF STABILITIES,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1968
- Accession Number
- AD0680761
Entities
People
- Stephen H. Davis
Organizations
- RAND Corporation