## Abstract

In this paper, we consider an inverse problem for a system of evolution equations. The inverse problem can also be interpreted as a exact control problem in the transition of a substance ** W**(

*x, t*) from a nonlocal state

*W*_{1}(

*x*) to another nonlocal state

*W*_{2}(

*x*). The control element is assumed to have a nonlocal form. We show the existence of the inverse problem in classes of entire functions with respect to the spatial variable by the constructive method. Explicit formulas of the unknown functions

**(**

*W**x, t*) and

**(**

*λ**x*) are presented.

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