The starting point for the derivation of the general characteristics of differential equations, boundary-value problems, and Green functions for diffusion-wave fields is the consideration of time-domain equations of diffusion. Owing to the relative simplicity and popularity of the thermal-wave field, in the first eight chapters consideration will be given to the time-dependent partial differential equation of heat conduction in three dimensions as a generator of the linear thermal-wave-field (TWF) partial differential equation and associated boundary-value problems. Besides, the TWF formalisms developed herein are directly applicable to the mathematics of a fast growing spectrum of disciplines which encompass diffusion waves [Mandelis, 2000]. Their most widespread application outside the main areas dealt with in this book is in the time-harmonic non-destructive evaluation with Eddy currents [L. B. Felsen and N. Marcuvitz, 1972; J. R. Bowler, 1999] and in applications to geophysical problems [W. A. SanFilipo and G. W. Hohmann, 1985]. Very recently, diffusion-wave methods have been developed in the study of organic compound migration in stratified media, which help clarify the transport of cyclic diffusive transients subject to harmonic boundary conditions [Trefry, 1999].
KeywordsGreen Function Laplace Transformation Dirac Delta Function Conduction Heat Transfer Impulsive Source
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