An Inverse Eigenvalue Problem and an Extremal Eigenvalue Problem
This talk presents results for two inverse problems which arise in the study of vibrating systems. The first problem (Part I) extends the theory of second order inverse eigenvalue problems in one dimension and is joint work with Carol Coleman. The second problem (Part II) solves an identification problem for composite membranes in n-dimensions; this work is joint work with Steven Cox.
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- L. Andersson, Inverse eigenvalue problems for a Sturm-Liouville equation in impedance form, Inverse Problems (4) (1988) 929–971.Google Scholar
- F. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York, 1974.Google Scholar
- C. Coleman, An Inverse Spectral Problem with a Rough Coefficient, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York.Google Scholar
- J. Poeschel and E. Trubowitz, Inverse Spectral Theory, Academic Press, 1987.Google Scholar
- G. Auchmuty, Dual Variational Principles for Eigenvalue Problems, in Nonlinear Functional Analysis and its Applications, F. Browder, ed., AMS 1986, 55–71.Google Scholar
- J. Cea and K. Malanowski, An example of a max-min problem in partial differential equations, SIAM J Control, (3) 305–316.Google Scholar
- S.J. Cox and J.R. McLaughlin, Extremal Eigenvalue Problems for Composite Membranes I, Appl Math and Optimization (to appear).Google Scholar
- S.J. Cox and J.R. McLaughlin, Extremal Eigenvalue Problems for Composite Membranes II, Appl Math and Optimization (to appear).Google Scholar
- M.G. Krein, On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability, AMS Translations Ser. 2 (1), (1955) 163–187.Google Scholar