Extremal methods for the solution of ill-posed problems and their applications to inverse problems of heat transfer. (Ehkstremal’nye metody resheniya nekorrektnykh zadach i ikh prilozheniya k obratnym zadacham teploobmena.) (Russian) Zbl 0657.35003

Alifanov, O. M.; Artyukhin, E. A.; Rumyantsev, S. V.

Moskva: Nauka. 288 p. R. 2.5 (1988).

This book is devoted to iterative regularization methods of ill-posed abstract problems as well as inverse problems of mathematical physics. The authors discuss different iterative gradient algorithms of solving of linear and nonlinear problems and their regularization that is realized with stopping of iterative process in according to agreement condition between the iterate number and the error of initial data, the applying of abstract results to analyse the linear and nonlinear, one-dimensional and multidimensional, fixed and moving boundary value inverse problems for the heat conductivity equations (these problems describe concrete problems of heat exchange and heat transfer and so on), and designs of the physical experiments in these problems having to increase the information that can be received with these experiments.
The book consists of 6 chapters: The identification problem and inverse problems in processes of heat transfer; The iterative regularization of ill-posed problems; The general theory of gradient algorithms for solving of heat exchange inverse problems; The iterative methods of solving of the heat conductivity problems; The solving algorithms for some inverse problems; The design of experiments in the solving theory for the heat exchange inverse problems. A short appendix contains some results in the theory of operators in Hilbert spaces. The bibliography contains 238 items.
The book is destined for specialists, graduate and post graduate students in the fields of numerical and computer mathematics, physics of heat transfer processes, heat engineering and so on.

Reviewer: P.P.Zabrejko

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35R30	Inverse problems for PDEs
35R25	Ill-posed problems for PDEs
80A20	Heat and mass transfer, heat flow (MSC2010)
35B40	Asymptotic behavior of solutions to PDEs
35B65	Smoothness and regularity of solutions to PDEs
35K05	Heat equation
47J25	Iterative procedures involving nonlinear operators

Keywords:

iterative regularization; ill-posed; inverse problems; mathematical physics; gradient algorithms; initial data; heat conductivity; identification; Hilbert spaces; bibliography