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Electromagnetism of Continuous MediaMathematical Modelling and Applications$
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Mauro Fabrizio and Angelo Morro

Print publication date: 2003

Print ISBN-13: 9780198527008

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198527008.001.0001

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Existence and uniqueness

Existence and uniqueness

Chapter:
(p.297) Chapter 7 Existence and uniqueness
Source:
Electromagnetism of Continuous Media
Author(s):

Mauro Fabrizio

Morro Angelo

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527008.003.0007

This chapter provides a wide class of mathematical problems which originates from the application of Maxwell’s differential equations to electromagnetic systems. Static, stationary, and transient problems are investigated for dielectrics or conductors with instantaneous response or with memory, subject to various boundary conditions. The main concern is to establish existence, uniqueness, and stability of the solution. This objective is realized by applying different mathematical techniques both to adhere to the features of the model and to offer a profitable set of approaches.

Keywords:   static solutions, stationary solutions, quasi-static problem, evolution problem, asymptotic behaviour, spatial decay

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