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Multidimensional Inverse and Ill-Posed Problems for Differential Equations (Hardcover, Reprint 2014)
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Multidimensional Inverse and Ill-Posed Problems for Differential Equations (Hardcover, Reprint 2014)
Series: Inverse and Ill-Posed Problems Series
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Inverse problems are usually nonlinear and are separated into
one-dimensional and multidimensional problems, depending on whether
the sought function (or functions) is a function of one variable or
of many. Multidimensionality of inverse problems has particular
value at present, because practice shows that many investigating
processes are described by an equation, of which the co-efficient
essentially depends on many variables. This monograph is devoted to
statements of multidimensional inverse problems, in particular to
methods of their investigation. Questions of the uniqueness of
solution, solvability and stability are studied. Methods to
construct a solution are given and, in certain cases, inversion
formulas are given as well. Concrete applications of the theory
developed here are also given. Where possible, the author has
stopped to consider the method of investigation of the problems,
thereby sometimes losing generality and quantity of the problems,
which can be examined by such a method. The book should be of
interet to researchers in the field of applied mathematics,
geophysics and mathematical biology.
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