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Inverse problems for second-order differential pencils with Dirichlet boundary conditions
-
Sergey A. Buterin
and
Vjacheslav A. Yurko
Published/Copyright:
December 14, 2012
Abstract.
Inverse spectral problems are studied for second-order differential pencils on a finite interval with arbitrary behavior of the spectrum. The spectral data introduced generalize the classical discrete spectral data corresponding to the specification of the spectral function for the selfadjoint Sturm–Liouville operator. The connection with other types of spectral characteristics is investigated. By the method of spectral mappings a uniqueness theorem is proved and constructive procedures for solving the inverse problem are obtained.
Keywords: Second-order differential pencils; diffusion operator; inverse spectral problems; method
of spectral mappings; generalized weight numbers
Received: 2012-09-14
Published Online: 2012-12-14
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Second-order differential pencils;
diffusion operator;
inverse spectral problems;
method
of spectral mappings;
generalized weight numbers
Articles in the same Issue
- Masthead
- Extra-optimal methods for solving ill-posed problems
- Regularization for ill-posed parabolic evolution problems
- Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity
- On some identification problem for source function to one semievolutionary system
- Regularization of backward parabolic equations in Banach spaces
- On the existence of global saturation for spectral regularization methods with optimal qualification
- Inverse determination of unsteady temperatures and heat fluxes on inaccessible boundaries
- Well-posedness of the Cauchy problem to a nonlinear magnetoelastic system in 1-D periodic media
- A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data
- Inverse problems for second-order differential pencils with Dirichlet boundary conditions
