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Quadratic optimization in Banach spaces is explored in the context of ill-posedness. We elucidate the conditions under which the cost function is bounded from below. Issues related to the ill-posedness in Hilbert scales have been comprehensively studied in a constructive way in Inverse Probl. 24...
Inverse problems of spectral analysis are studied for Sturm–Liouville differential operators on arbitrary compact graphs. The uniqueness of recovering operators from their spectra is proved, and a constructive procedure for the solution of this class of inverse problems is provided.
We consider the problem of quantitative non-destructive evaluation of corrosion in a 2D domain representing a thin metallic plate. Corrosion damage is assumed to occur in an inaccessible part of the domain. Reconstruction of the damaged profile is possible by measuring an electrostatic current...
In a framework of classical one-dimensional binary alloy solidification problem with zero diffusion coefficient in the solid phase the inverse problem is posed and considered. The problem consists in finding of the temperature regime at the outer boundary of domain when the final distribution of...
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