On the Principle of Exchange of Stabilities.

Stephen H. Davis

ResearchPublished 1968

Proof of a perturbation theorem: A class of real, bounded (non-self-adjoint) 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; hence, if epsilon is less than the critical value, traveling waves-- whether growing or decaying--are forbidden. 59 pp. Refs. (Author

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  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1968
  • Document Number: RM-5695-PR

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Davis, Stephen H., On the Principle of Exchange of Stabilities. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/research_memoranda/RM5695.html.
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