### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Quantum Studies: Mathematics and Foundations |

Early online date | 24 Apr 2019 |

DOIs | |

Publication status | E-pub ahead of print - 24 Apr 2019 |

### Fingerprint

### Keywords

- homogenisation
- evolutionary equations
- G-convergence
- H-convergence
- nonlocal H-convergence
- heat conduction
- wave equation
- Maxwell's equations

### Cite this

*Quantum Studies: Mathematics and Foundations*, 1-22. https://doi.org/10.1007/s40509-019-00192-8

}

*Quantum Studies: Mathematics and Foundations*, pp. 1-22. https://doi.org/10.1007/s40509-019-00192-8

**Homogenisation and the weak operator topology.** / Waurick, Marcus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homogenisation and the weak operator topology

AU - Waurick, Marcus

PY - 2019/4/24

Y1 - 2019/4/24

N2 - This article surveys results that relate homogenisation problems for partial differential equations and convergence in the weak operator topology of a suitable choice of linear operators. More precisely, well-known notions like G-convergence, H-convergence as well as the recent notion of nonlocal H-convergence are discussed and characterised by certain convergence statements under the weak operator topology. Having introduced and described these notions predominantly made for static or variational type problems, we further study these convergences in the context of dynamic equations like the heat equation, the wave equation or Maxwell’s equations. The survey is intended to clarify the ideas and highlight the operator theoretic aspects of homogenisation theory in the autonomous case.

AB - This article surveys results that relate homogenisation problems for partial differential equations and convergence in the weak operator topology of a suitable choice of linear operators. More precisely, well-known notions like G-convergence, H-convergence as well as the recent notion of nonlocal H-convergence are discussed and characterised by certain convergence statements under the weak operator topology. Having introduced and described these notions predominantly made for static or variational type problems, we further study these convergences in the context of dynamic equations like the heat equation, the wave equation or Maxwell’s equations. The survey is intended to clarify the ideas and highlight the operator theoretic aspects of homogenisation theory in the autonomous case.

KW - homogenisation

KW - evolutionary equations

KW - G-convergence

KW - H-convergence

KW - nonlocal H-convergence

KW - heat conduction

KW - wave equation

KW - Maxwell's equations

UR - https://link.springer.com/journal/40509

U2 - 10.1007/s40509-019-00192-8

DO - 10.1007/s40509-019-00192-8

M3 - Article

SP - 1

EP - 22

ER -