Abstract
The idea of extending the Liapunov function technique to examine stability problems of partial differential equations was first proposed by Zubov [1] and Movchan [2] in 1959, but until recently there have been few applications to physical problems. A useful bibliography is that of Wang [3], and a theoretical background using Hilbert and Sobolev spaces has been given by Buis, Vogt et al. [4]. In the present paper some specific applications are reviewed, and a useful method for constructing Liapunov functionals is suggested.
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References
Zubov, V. I.: The Methods of Liapunov and their Application, Leningrad 1959.
Movchan, A. A.: Prikl. Mat. Mekh. 23, 483 (1959).
Wang, P. K. C.: Int. J. Control 7, 101 (1968).
Buis, G. R., Vogt, W. G.: Lyapunov stability for partial differential equations. NASA CR-1100, 1968.
Kolmogorov, A. N., Fomin, S. V.: Functional Analysis,Vol. I, Rochester, N.Y.: Graylock Press 1957.
Kalman, R. E., Bertram, J. E.: Trans. A.S.M.E. D 82, 371 (1960).
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Pritchard, A. J.: J. Inst. Maths. Applies. 4, 78 (1968).
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability, Oxford: Clarendon Press 1961.
Parks, P. C., Pritchard, A. J.: Proc. 4th IFAC Congress, Warsaw 1969, Paper 20. 5.
Parks, P. C.: IEEE Trans. Autom. Control AC-11, 334 (1966).
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© 1971 Springer-Verlag, Berlin/Heidelberg
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Parks, P.C. (1971). Some Applications of Liapunov Functionals. In: Leipholz, H. (eds) Instability of Continuous Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65073-4_18
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DOI: https://doi.org/10.1007/978-3-642-65073-4_18
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