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This monograph deals 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.

Evolution equations. --- Inverse problems (Differential equations) --- Differential equations --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Coefficients. --- Concrete Inverse Problems. --- Differential-difference Equations. --- Kinetic Evolution Equations. --- Linear Statements. --- Multidimensional Inverse Problems. --- Nonlinear Evolution Equations. --- Nonlinear Statements. --- Second Order Equations. --- Transfer Equations.

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Mathematics

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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 interest to researchers in the field of applied mathematics, geophysics and mathematical biology.

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Mathematics

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