Titlebook: Introduction to Inverse Problems for Differential Equations; Alemdar Hasanov Hasano?lu,Vladimir G. Romanov Book 2021Latest edition Springe

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Inverse Source Problems with Final Overdeterminationdimensional heat equation has first been considered by A.N. Tikhonov in study of geophysical problems [.]. In this work the heat equation with prescribed lateral and final data is studied in half-plane and the uniqueness of the bounded solution is proved.

財(cái)主

Inverse Problems for Elliptic Equationsmography problem which is studied in the next chapter. In the second part of the chapter, the Dirichlet-to-Neumann operator is introduced. It is proved that this operator uniquely defines the potential .(.) in Δ.(.)?+?.(.)?=?0.

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Inverse Problems for Damped Wave Equationsifying the unknown principal coefficient .(.) from Dirichlet-to-Neumann operator, and the inverse problem of recovering the unknown potential .(.) from either from Neumann-to-Dirichlet or Dirichlet-to-Neumann operators.

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Inverse Problems for Parabolic Equationsbolic equations through the corresponding solutions of inverse problems for hyperbolic equations, using the Laplace transform. In the final part of this chapter, we study the relationship between the inverse problems for parabolic equation and inverse spectral problems.

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ginning graduate students.Can be used as a backbone for a le.This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenome

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CRUC

Introduction Ill-Posedness of Inverse Problems, of these models are governed by differential and integral equations. If all the necessary inputs in these models are known, then the solution can be computed and behavior of the physical system under various conditions can be predicted. In terms of differential problems, the necessary inputs includ

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Inverse Source Problems with Final Overdeterminationons in various fields of science and technology. These problems play a key role in providing estimations of unknown and inaccessible source terms involved in the associated mathematical model, using some measured output. An inverse problem with the final overdetermination ..?:=?.(.), .?>?0, for one-

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Inverse Problems for Hyperbolic Equations?..?=?.(., .).(.) for the quarter plane ., with Dirichlet type measured output .(.)?:=?.(., .)|.. The time-dependent source .(.) and the spacewise-dependent source .(.) are assumed to be unknown in these inverse problems.