Abstract
We consider the heat equation in the N-dimensional Euclidean space R^N the half space of R^N or the exterior domain of a ball, and study the large time behavior of hot spots of the solutions. The large time behavior of hot spots depends on the shape of domains and the boundary conditions. Furthermore we study the large time behavior of hot spots of the solutions of the heat equation with a potential. Then we see that the behavior of hot spots depends on the behavior of positive stationary solutions at the spacial infinity.
