Abstract
On a stability of a solution of the loaded heat equationSteadily 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 Ω ≡ (-π/2, π/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(-σ0t) as t → ∞.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.