Estimates of the age of a heat distribution

Abstract

The paper deals with the possibility to solve the heat equation backwards in time. More specifically, we treat the following problem. Given the temperature at a finite number of points of a homogeneous bar, how old can the heat distribution be? In the case that the temperature is given at equidistant points x₁, the problem is completely solved. In the case of nonequidistant x_i we find an upper bound for the age. Such a bound is also obtained when the information about the heat distribution is given by the value of a finite number of linear functionals.