Abstract
In this paper, we consider the heat equation with a time-varying delays term in the boundary condition in a bounded domain of R-n, the boundary Gamma is a class C-2 such that Gamma = Gamma(D) boolean OR Gamma(N), with (Gamma(D)) over bar boolean AND (Gamma(N)) over bar = theta, Gamma(D) not equal 0 and Gamma(N) not equal 0. Well-posedness of the problems is analyzed by using semigroup theory. The exponential stability of the problem is proved. This paper extends in n-dimensional the results of the heat equation obtained in [11].