Nonlinear Inverse Problems

Abstract

In the previous chapters, we considered linear problems which we wrote as Kx= y, where K was a linear and (often) compact operator between Hilbert spaces. Needless to say that most problems in applications are nonlinear. For example, even in the case of a linear differential equation of the form - u″+ cu= f for the function u the dependence of u on the parameter function c is nonlinear; that is, the mapping c↦ u is nonlinear. In Chapters 5, 6, and 7 we will study particular nonlinear problems to determine parameters of an ordinary or partial differential equation from the knowledge of the solution.