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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.
This monographdeals with methods of studying multidimensional
inverse problems for kinetic and other evolution equations, in
particular transfer equations. The methods used are applied to
concrete inverse problems, especially multidimensional inverse
problems applicable in linear and nonlinear statements. A
significant part of the book contains formulas and relations for
solving inverse problems, including formulas for the solution and
coefficients of kinetic equations, differential-difference
equations, nonlinear evolution equations, and second order
equations.
The Inverse and Ill-Posed Problems Series is a series of monographs
publishing postgraduate level information on inverse and ill-posed
problems for an international readership of professional scientists
and researchers. The series aims to publish works which involve
both theory and applications in, e.g., physics, medicine,
geophysics, acoustics, electrodynamics, tomography, and ecology.
M.M. Lavrentiev is the author of many fundamental scientific
results in many directions of mathematics and its applications,
such as differential equations, inverse and ill-posed problems,
tomography, numerical and applied mathematics. His results in the
theory of inverse problems for differential equations and in
tomography are well known all over the world.
To honour him on the occasion of his 70th birthday renowned
scientists in this field of mathematics, both from East and West,
have contributed to this special collection of papers on ill-posed
and inverse problems, which will be of interest to anyone working
in this field.
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