### SOLUTION TO THE INITIAL-FINAL VALUE PROBLEM FOR A NON-STATIONARY LEONTIEF TYPE SYSTEM

#### Abstract

The article is devoted to the construction of a solution to the initial-final value problem for a non-stationary Leontief type system. Such systems take place in dynamic balance models of the economy. A distinctive feature of Leontief type systems is the degeneracy of the matrix at the time derivative, due to the fact that some types of resources of economic systems cannot be stored. In addition, dynamic balance systems of the economy are often described using time-dependent coefficients. We use resolving streams of matrices to construct solutions for such systems. In addition, the initial-final value condition is used instead of the standard initial condition. For economic systems, the initial-final value condition can be interpreted as taking into account not only indicators at the initial moment of time, but also indicators that are achieved at the final moment of time.

#### Keywords

Sobolev type equations; spectral projector; relatively regular matrices; flows of solving matrices

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