In this book, the authors present a number of examples which lead to ill-posed problems arising with the processing and interpretation of data of physical measurements. Basic postulates and some results in the general theory of ill-posed problems follow. The exposition also includes problems of analytic continuation from continua and discrete sets, analogous problems of continuation of solutions of elliptic and parabolic equations, the main ill-posed boundary value problem for partial differential equations, and results on the theory of Volterra equations of the first kind. A very broad presentation is given of modern results on the problem of uniqueness in integral geometry and on inverse problems for partial differential equations.
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978-0-8218-0896-2 (9780821808962)
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Schweitzer Klassifikation
Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations.
