Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces (Q1920762)

A nonlinear multidimensional inverse problem for an evolution equation of a general type is considered. The problem under consideration can be reduced to two problems with initial data for evolution equations in a Hilbert space. One of the transformed problems is nonlinear, the other linear. Since the initial data for the transformed problems are uniquely determined by the information that is given in the inverse problem, this allows constructing solutions of the inverse problem by the proposed approach. In some case, explicit formulae for a solution to the inverse problem can be written down.