Upper bounds for the fundamental eigenvalue for a domain of unknown shape
- 46 Downloads
For a particular eigenvalue problem in partial differential equations, upper bounds are established which do not depend on the shape of the domain but only on its size. The problem describes the free sloshing motions of an incompressible, inviscid fluid in a canal and furnishes upper bounds to the highest fundamental sloshing frequency which is attainable for a given cross-section area of the canal.
KeywordsTrial Function Isoperimetric Inequality Restricted Problem Rayleigh Quotient Isoperimetric Problem
Unable to display preview. Download preview PDF.
- 1.Payne, L. E.,Isoperimetric Inequalities and Their Applications, SIAM Review, Vol. 9, No. 3, 1967.Google Scholar
- 3.Weinberger, H. F.,An Isoperimetric Inequality for the N-Dimensional Free Membrane Problem, Journal of Rational Mechanics and Analysis, Vol. 5, No. 4, 1956.Google Scholar
- 4.Troesch, B. A.,An Isoperimetric Sloshing Problem, Communications on Pure and Applied Mathematics, Vol. 18, No. 1/2, 1965.Google Scholar
- 5.Abramson, H. N., Editor,The Dynamic Behavior of Liquids in Moving Containers, National Aeronautics and Space Administration, NASA Report No. SP-106, 1966.Google Scholar
- 6.Moiseev, N. N.,Introduction to the Theory of Liquid-Containing Bodies, Advances in Applied Mechanics, Vol. 8, Edited by G. Kuerti, Academic Press, New York, New York, 1964.Google Scholar
- 7.Henrici, P., Troesch, B. A., andWuytack, L.,Sloshing Frequencies for a Half-Space with Circular or Strip-Like Aperture, Journal of Applied Mathematics and Physics (ZAMP), Vol. 21, No. 3, 1970.Google Scholar
- 8.Budiansky, B.,Sloshing of Liquids in Circular Canals and Spherical Tanks, Journal of the Aero-Space Sciences, Vol. 27, No. 2, 1960.Google Scholar