Stabilization of Solutions of Two-Dimensional Parabolic Equations and Related Spectral Problems

Abstract

One of the important properties that characterize the behaviour of solutions of boundary value problems for differential equations is stabilization, which has a direct relationship with the problems of controllability. In this paper, the problems of solvability are investigated for stabilization problems of two-dimensional loaded equations of parabolic type with the help of feedback control given on the boundary of the region. These equations have numerous applications in the study of inverse problems for differential equations. The spectral properties of the loaded two-dimensional Laplace operator, which are used to solve the initial stabilization problem, are also studied.