Abstract:
Steadily growing interest in study of loaded differential equations is explained by the range of their
applications and a circumstance that loaded equations make a special class of functional-differential equations
with specific problems. These equations have applications in study of inverse problems of differential
equations with important applied interests. In this paper solvability questions of stabilization problems
with a boundary for the loaded heat equation are studied in the given bounded domain ( =2; =2).
The task is to choose boundary conditions (controls), that the solution of the obtained mixed boundary
value problem tends to a given stationary solution with the prescribed speed exp( 0t) as t ! 1. At this
the control is required to be a feedback control, i.e. that it reacted to the unintended fluctuations of the
system, suppressing the results of their impact on the stabilized solution. Stabilization problems have a
direct connection with controllability problems. The paper proposes a mathematical formalization of the
concept of feedback, and with its help it solves the problem of stabilizability of a loaded heat equation by
dint of feedback control given on the part of the boundary is solved.
