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
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.

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 |