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Abstract <p> In this paper, we study an optimal control problem of the value of a solution to an elliptic equation in a bounded domain with a smooth boundary by means of a flow through the domain boundary. We consider the operator of the equation, which is the sum of the Laplace operator with a small coefficient and a zero-order operator. The control is constrained by an integral relation. As a performance index, we employ the sum of the squared norm of the deviation of a state from a prescribed state on the domain boundary and the squared norm of the control. We obtain a complete asymptotic expansion of the solution to the problem in powers of the small parameter. </p>

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Asymptotics of a Solution to an Optimal Boundary Control Problem with Performance Index Defined on the Boundary

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. R. Danilin,
  • I. V. Pershin

摘要

Abstract

In this paper, we study an optimal control problem of the value of a solution to an elliptic equation in a bounded domain with a smooth boundary by means of a flow through the domain boundary. We consider the operator of the equation, which is the sum of the Laplace operator with a small coefficient and a zero-order operator. The control is constrained by an integral relation. As a performance index, we employ the sum of the squared norm of the deviation of a state from a prescribed state on the domain boundary and the squared norm of the control. We obtain a complete asymptotic expansion of the solution to the problem in powers of the small parameter.