A non‐autonomous model for the evolution of electromagnetic fields in complex media‡. (19th June 2013)

• Record Type: Journal Article
• Authors: Liaskos, K. B.; Barbatis, Gerassimos; Stratis, Ioannis
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 2(2014:Jan. 30)
• Page Start: 245
• Page End: 250
• Publication Date: 2013-06-19
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2842
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2842-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this work, some results on a non‐autonomous, local in time, approximation of the constitutive laws for the evolution of electromagnetic fields in complex media, in the time domain, are presented. The initial‐boundary value problem for Maxwell's equations in a bounded domain, supplemented with these approximating constitutive relations, reduces to a Cauchy problem for an ODE (i.e. a non‐autonomous Sobolev equation of pseudo‐parabolic type) in a suitable Hilbert space. Under appropriate assumptions, well‐posedness results are established. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>