Ole H Hald and Joyce R McLaughlin 1998 Inverse Problems 14 245 doi:10.1088/0266-5611/14/2/003
Inverse problems: recovery of BV coefficients from nodes
Ole H Hald
and Joyce R McLaughlin
We consider the Sturm-Liouville problem on a finite interval with Dirichlet boundary conditions. Let the elastic modulus and the density be of bounded variation. Results for both the forward problem and the inverse problem are established. For the forward problem, new bounds are established for the eigenfrequencies. The bounds are sharp. For the inverse problem, it is shown that the elastic modulus is uniquely determined, up to one arbitrary constant, by a dense subset of the nodes of the eigenfunctions when the density is known. Similarly it is shown that the density is uniquely determined, up to one arbitrary constant, by a dense subset of the nodes of the eigenfunctions when the elastic modulus is known. Algorithms for finding piecewise constant approximations to the unknown elastic modulus or density are established and are shown to converge to the unknown function at every point of continuity. Results from numerical calculations are presented.
- PACS
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46.70.Hg Membranes, rods and strings
02.60.Gf Algorithms for functional approximation
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65F18 Inverse eigenvalue problems
- Subjects
- Dates
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Issue 2 (April 1998)
Received 24 September 1997
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Inverse problems: recovery of BV coefficients from nodes
Ole H Hald and Joyce R McLaughlin 1998 Inverse Problems 14 245
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