### Abstract

The idea of monotonicity is shown to be the central theme of the solution theories associated with problems of mathematical physics. A “grand unified” setting is surveyed covering a comprehensive class of such problems. We illustrate the applicability of this setting with a number of examples. A brief discussion of stability and homogenization issues within this framework is also included.

Original language | English |
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Title of host publication | Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics |

Editors | Wolfgang Arendt, Ralph Chill, Yuri Tomilov |

Place of Publication | Heidelberg |

Publisher | Springer |

Pages | 397-452 |

Number of pages | 56 |

ISBN (Print) | 9783319184937 |

DOIs | |

Publication status | Published - 20 Dec 2015 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Publisher | Springer |

Volume | 250 |

ISSN (Print) | 0255-0156 |

### Keywords

- well-posedness
- monotonicity
- homogenization
- stability

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## Cite this

Picard, R., Trostorff, S., & Waurick, M. (2015). Well-posedness viaMonotonicity—an overview. In W. Arendt, R. Chill, & Y. Tomilov (Eds.),

*Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics*(pp. 397-452). (Operator Theory: Advances and Applications; Vol. 250). Heidelberg: Springer. https://doi.org/10.1007/978-3-319-18494-4