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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
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G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

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Well Posedness

Well Posedness

Chapter:
(p.247) Chapter Twelve Well Posedness
Source:
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author(s):

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142173.003.0012

This chapter first presents a model for the Maxwell equations for complex random media in terms of stochastic integrodifferential equations. It then provides the appropriate functional framework that can allow for the treatment of the problem as an abstract stochastic integrodifferential equation in Hilbert space. In exploiting this framework, the chapter provides some solvability and well-posedness results for this model, using a semigroup-based approach. Hereafter, this chapter proposes alternative approaches to solvability and well posedness for the stochastic integrodifferential equations that arise in the modelling of random complex electromagnetic media, using either the finite-dimensional approximation (Faedo-Galerkin method) or the Wiener chaos approach.

Keywords:   well posedness, Maxwell equations, stochastic integrodifferential equations, solvability, semigroup-based approach, random complex electromagnetic media, finite-dimensional approximation, Faedo-Galerkin approach, Wiener chaos approach, Hilbert space

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