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

Rodríguez Bernal, Aníbal; Domínguez de Tena, Joaquín

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

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Publication date

2023

Authors

Rodríguez Bernal, Aníbal

Domínguez de Tena, Joaquín

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URI

https://hdl.handle.net/20.500.14352/88909

Abstract

In this work, we study the decay of mass for solutions to the heat equation in exterior domains, i.e., domains which are the complement of a compact set in RN . Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann conditions. We determine the exact amount of mass loss and identify criteria for complete mass decay, in which the dimension of the space plays a key role. Furthermore, the paper provides explicit mass decay rates.