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In this work, we study the decay of mass for solutions to the heat equationin exterior domains, i.e., domains which are the complement of a compact set in$\mathbb{R}^N$. Different homogeneous boundary conditions are considered,including Dirichlet, Robin, and Neumann conditions. We determine the exactamount of mass loss and identify criteria for complete mass decay, in which thedimension of the space plays a key role. Furthermore, the paper providesexplicit mass decay rates.

On the loss of mass for the heat equation in an exterior domain with general boundary conditions