On a time-optimal control problem for a heat conduction equation with involution
Abstract
In this paper, we consider a boundary control problem for a heat conduction equation with involution in a bounded one-dimensional domain.The solution with the control function on the border of the rod is given.The constraints on the control are determined to ensure that the average value of the solution within the considered domain attains a given value.The considered control problem is reduced to the Volterra integral equation, which is the first type, using the Fourier method.The proof of the existence of admissible control is related to the existence of a solution of the integral equation.The existence of the control function was proved by the Laplace transform method, and the estimate of the minimum time to reach the given average temperature in the rod was found.