### Abstract

Let K be a compact subset in Euclidean space R-m, and let E-K(t) denote the total amount of heat in R-m\K at time t, if K is kept at fixed temperature 1 for all tgreater than or equal to0, and if R-m\K has initial temperature 0. For two disjoint compact subsets K-1 And K-2 we define the heat exchange H-K 1,H- K2 (t)=E-K 1 (t)+E-K 2 (t)-E-K 1boolean ORK 2 (t). We obtain the leading asymptotic behaviour of HK,,K2(t) as t-->0 under mild regularity conditions on K-1 and K-2. (C) 2003 Elsevier Inc. All rights reserved.

Translated title of the contribution | Asymptotics of the heat exchange |
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Original language | English |

Pages (from-to) | 379 - 390 |

Number of pages | 12 |

Journal | Journal of Functional analysis |

Volume | 206 (2) |

DOIs | |

Publication status | Published - Jan 2004 |

### Bibliographical note

Publisher: Academic PressOther identifier: IDS number 761CU

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## Cite this

van den Berg, M. (2004). Asymptotics of the heat exchange.

*Journal of Functional analysis*,*206 (2)*, 379 - 390. https://doi.org/10.1016/j.jfa.2003.08.005