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On a multidimensional integral equation with data supported by low-dimensional analytic manifolds
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Mikhali Y. Kokurin
Veröffentlicht/Copyright:
1. Februar 2013
Abstract.
This paper is concerned with a 3D linear integral equation of the first kind which arises when solving nonlinear coefficient inverse problems for second order hyperbolic PDEs. We prove that the integral equation has at most one solution when its right part is given on appropriate analytic 2D and 1D manifolds. As compared to known uniqueness theorems, the dimension of a smooth manifold supporting problem data is decreased here from four to one. As auxiliary results, we give examples of 1D analytic manifolds of uniqueness and examples of minimal countable sets of uniqueness for harmonic functions in 3D domains.
Keywords: Hyperbolic equation; coefficient inverse problem; linear integral equation; uniqueness; harmonic function
Received: 2012-11-04
Published Online: 2013-02-01
Published in Print: 2013-02-01
© 2013 by Walter de Gruyter Berlin Boston
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Schlagwörter für diesen Artikel
Hyperbolic equation;
coefficient inverse problem;
linear integral equation;
uniqueness;
harmonic function
Artikel in diesem Heft
- Masthead
- Data regularization using Gaussian beams decomposition and sparse norms
- Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology
- The use of statistical tests to calibrate the normal SABR model
- Unique determination of potentials and semilinear terms of semilinear elliptic equations from partial Cauchy data
- Irregular nonlinear operator equations: Tikhonov's regularization and iterative approximation
- On a multidimensional integral equation with data supported by low-dimensional analytic manifolds
- Inverse problem for elliptic equation in a Banach space with Bitsadze–Samarsky boundary value conditions
- Certain problems of synchronization theory
