This book is devoted to an account of theories of heat conduction where the temperature may travel as a wave with a finite speed. The book surveys many of the theories which have been proposed as candidates to describe thermal motion as a wave. These theories are linked to solid mechanics (elasticity) and also to fluid mechanics.Wave motion in the form of acceleration waves and of shock waves is discussed. Numerical work in the area of thermal waves is also discussed. Analytical methods for establishing uniqueness, continuous dependence, growth, spatial decay and other results are described. Heat transfer in nanofluidics is considered as well as "hyperbolic heat theories" which are increasingly important in biology.
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