This book describes a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials-material substances whose properties are variable in space and time. The book discusses some general features of dynamic materials as thermodynamically open systems; it gives their adequate tensor description in the context of Maxwell's theory of moving dielectrics and makes a special emphasis on the theoretical analysis of spatio-temporal material composites (such as laminates and checkerboard structures). Some unusual applications are listed along with the discussion of some typical optimization problems in space-time via dynamic materials. This book will interest applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations; researchers in the field of smart metamaterials and their applications to optimal material design in dynamics.

Novel exposition of new mathematical theory developed by the author

Inhalt
A General Concept of Dynamic Materials.- An Activated Elastic Bar: Effective Properties.- Dynamic Materials in Electrodynamics of Moving Dielectrics.- G-closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation.- Rectangular Microstructures in Space-Time.- Some Applications of Dynamic Materials in Electrical Engineering and Optimal Design.