Boundary Control Problem for the Heat Equation with a Nonlocal Boundary Condition
In this paper, we study a boundary control problem for the one-dimensional heat
equation with a nonlocal boundary condition. The control is applied at one end of the domain, while
the temperature at the opposite boundary is linked to the temperature at a fixed interior point.
The control objective is formulated as an integral condition prescribing the average temperature of
the rod. Using the method of separation of variables, the problem is reduced to a Volterra integral
equation of the first kind. The existence of an admissible control function is proved by means of the
Laplace transform method.
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