Dear Colleagues,
We continue our Colloquium.

Thursday, November 11, 2:00 p.m. Metro 207.

Professor Maeve McCarthy, Myrray State University

"Recovery of a Density from the Eigenvalues of a Nonhomogeneous Membrane"

The vibrating elastic membrane is a classical problem in Mathematical
Physics which arises in a wide variety of physical applications. Since the
geometry of the membrane is usually well defined for a particular problem,
determination of the nature of any nonhomogeneity is critical. The
eigenvalues of particular membranes are often quite accessible
experimentally and so a method for the determination of the nonhomogeneity
based on the available eigenvalues is of practical importance.

Projection of the boundary value problem and its coefficients onto
appropriate vector spaces leads to a matrix inverse problem. Although the
matrix inverse problem is of nonstandard form, it can be solved by a
fixed-point iterative method. Convergence of the method for a rectangular
membrane is discussed and numerical evidence of the success of the method is
presented. The existence of multiple eigenvalues for certain rectangular
membranes causes the analysis to fail. However, the algorithm has been
adapted with some success.

http://www.math.murraystate.edu/mccarthy/

Comment. Prof. McCarthy is a serious specialist in PDE, Inverse Problem,
Optimal Design, and Calculus of Variations. We especially recommend her
talk to the physicists and engineers.
Boris Belinskiy,
Colloquium Committee
Boris Belinskiy
Department of Mathematics
University of Tennessee at Chattanooga
615 McCallie Ave
Chattanooga, TN 37403-2598
Ph. 423-755-4748
Fax 423-755-4586
e-mail [log in to unmask]