Stability of dissipative systems with applications to fluids and magnetofluids

  • E. M. Barston
Part 2. Stability Problems
Part of the Lecture Notes in Physics book series (LNP, volume 21)


An energy principle is presented which gives necessary and sufficient conditions for exponential stability for a useful class of continuous linear dissipative systems. The maximal growth rate Ω of an unstable system is shown to be the least upper bound of a certain functional, providing a variational expression for Ω. Applications to the problems of the stability of a stratified viscous incompressible fluid in a gravitational field and the resistive, viscous, incompressible magnetohydrodynamic sheet pinch are discussed.


Maximum Principle Exponential Stability Maximal Growth Rate Energy Principle Unstable System 
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Copyright information

© Springer Verlag 1973

Authors and Affiliations

  • E. M. Barston
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew York

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