Mathematical methods in electromagnetism and related topics
 Organizer(s):
Name:
Affiliation:
Country:
Ioannis Stratis
National and Kapodistrian University of Athens
Greece
Pier Domenico Lamberti
University of Padua (Università degli Studi di Padova)
Italy
 Introduction:  
  The proposed session will mainly focus on various mathematical aspects of electromagnetism and Maxwell`s equations, as well as related problems, from modeling issues to well-posedness results. Various constitutive laws will be presented, linear and nonlinear, local and non-local. The domains considered will vary from very regular to Lipschitz and to fractal. The relevant function spaces will be considered, with an emphasis on boundary and topological conditions. Basic and advanced tools to solve problems of electromagnetism in their natural functional frameworks will be taken into consideration, and mathematical methods (e.g., boundary integral methods, semigroups, functional and variational methods, etc.,) will be employed. As examples of applications of these tools and concepts, several fundamental problems of electromagnetism, stationary or time-dependent, will be considered: scattering of an incident wave by obstacles, bounded or not; wave propagation in waveguides; homogenization problems; optimization problems. Suitable numerical methods will of course be also considered. Mathematical notions allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials.