Abstract
The asymptotic stability result obtained by Pritchard for the Benard and Taylor problems employing the Liapunov-Movchan theory is optimized by using inequalities and variational techniques. The equivalence between this result and the one obtained by the energy theory is demonstrated. Future applications as related to the symmetry of the operators are discussed.
Zusammenfassung
Die asymptotischen Stabilitätsresultate von Prichard für die Benard-und Taylor-Probleme, die mit Hilfe der Liapunov-Movchan-Theorie erhalten worden sind, werden durch Ungleichungen und Methoden der Variationsrechnung optimiert. Die Aequivalenz zwischen diesem Resultat und dem Ergebnis der Energiemethode wird nachgewiesen. Mögliche Anwendungen werden diskutiert, die sich auf die Symmetrie der Operatoren beziehen.
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Sinha, S.C., Carmi, S. On the Liapunov-Movchan and the energy theories of stability. Journal of Applied Mathematics and Physics (ZAMP) 27, 607–612 (1976). https://doi.org/10.1007/BF01591172
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DOI: https://doi.org/10.1007/BF01591172