Uniqueness in exterior domains for the generalized heat conduction (Q1861790)

Uniqueness of solutions of the linear hyperbolic heat conduction equation in the case of unbounded domains is studied in the paper. In the case of the forward-in-time problem, the uniqueness is proved by means of the weighted energy method for the solutions, which increase as the exponential of the square of distance from the origin. For the backward-in-time problem, the uniqueness holds for the solutions, which increase as the exponential of the distance from the origin. In this case, an additional condition is also used.