2014/05/22 by Andrzej Hanyga, Hanyga, Andrzej
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1405.5724
arxiv created 2015/07/01 · arxiv updated 2015/07/02
We extend the theory of complete Bernstein functions to matrix-valued functions and apply it to analyze Green's function of an anisotropic multi-dimension\-al linear viscoelastic problem. Green's function is given by the superposition of plane waves. Each plane wave is expressed in terms of matrix-valued attenuation and dispersion functions given in terms of a matrix-valued positive semi-definite Radon measure. More explicit formulae are obtained for 3D isotropic viscoelastic Green's functions. As an example of an anisotropic medium the transversely isotropic medium with a constant symmetry axis is considered.