Uniqueness in exterior domains for the generalized heat conduction

Abstract

In this note, we prove uniqueness of those solutions of the generalized heat conduction equation that increase as an exponential of the square of the distance from the origin. Continuous dependence results with respect to initial data and supply terms are also proved. The results are obtained with the help of the weighted energy method. We also prove uniqueness of the solutions of the backward in time problem. This second result is obtained by means of the weighted Lagrange identities method.