Inverse problems in mathematical physics
Abstract
Procedures for the correct formulation and solution of inverse problems, which usually belong to the class of ill-posed problems, are discussed. Attention is given to the concept of the conditionally correct statement of a problem, the concept of quasi-solution, and the fundamentals of regularization theory. The discussion also covers the uniqueness of solutions to inverse problems in mathematical physics, with consideration given to problems involving layered media, impedance problems, gravimetric problems, and inverse problems of heat conduction. The problem of stability and regularizing operators are also discussed.
- Publication:
-
Moscow Izdatel Moskovskogo Universiteta Pt
- Pub Date:
- 1984
- Bibcode:
- 1984MIzMU....R....G
- Keywords:
-
- Boundary Value Problems;
- Geophysics;
- Inverse Scattering;
- Mathematical Models;
- Physics;
- Analysis (Mathematics);
- Boundary Layers;
- Conductive Heat Transfer;
- Control Theory;
- Gravimetry;
- Numerical Stability;
- Operators (Mathematics);
- Seismology;
- Uniqueness Theorem;
- Physics (General)