Yu. E. Anikonov

Formulas in Inverse and Ill-Posed Problems - Inverse and Ill-Posed Problems Series Yu. E. Anikonov Reprint 2014 edition

This monograph is devoted to constructive investigation methods of multidimensional, mainly non-linear, inverse problems for evolution equations. The author has discovered various explicit formulas which determine solutions of inverse problems. These formulas contain arbitrary formulas which determine solutions of inverse problems. These formulas contain arbitrary functions and functions which satisfy some differential equations. Numerous results on simultaneous determination of co-efficients and solutions of differential equations and inequalities are provided in the book. It also contains new differential and integro-differential equations, as well as the reduction of multidimensional inverse problems to the initial boundary for these equations. The methods and results of multidimensional inverse problems theory for evolution equations are, and will continue to be, important tools in various kinds of engineering, planning, control and identification situations. This monograph, together with the author's previous monograph in the series, "Multidimensional Inverse and Ill-Posed Problems for Differential Equations", provide a wide collection of investigation methods in this field, and should be of interest to researchers in these and related subjects.