Volterra Equations of the First kind with Discontinuous Kernels in the Theory of Evolving Systems Control

Details Volterra Equations of the First kind with Discontinuous Kernels in the Theory of Evolving Systems Control Volterra Equations of the First kind with Discontinuous Kernels in the Theory of Evolving Systems Control

2011-11-25

arxiv.org/abs/1111.5903v1

Mathematics

Optimization and Control

11 pages, bibl 14, Submitted to Studia Informatica Universalis

Scientific paper

The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing approximations of parametric families of solutions of such equations is suggested. The parametric family of solutions is constructed in terms of a logarithmic-power asymptotics.

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