On the boundary control problem associated with a fourth order parabolic equation in a two-dimensional domain

In this paper, we consider a boundary control problem associated with a fourth order parabolic type equation in a bounded two-dimensional domain. The solution with the control function on the border of the considered domain 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 initial-boundary problem is solved by the Fourier method, and the control problem under consideration is analyzed with the Volterra integral equation. The existence of admissible control is proved by the Laplace transform method.

Ҳали таржима қилинмаган