Finite Propagation Speed of Waves in Anisotropic Viscoelastic Media

Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical imaging of tissue, in particular in the supersonic imaging experiment, and also in geophysics and ocean acoustics. With these applications in mind, noting that there are many other applications as well, we present finite propagation speed results for very general integro-differential, anisotropic, viscoelastic linear models, which are not necessarily of convolution type. We start with work density, define work density decomposition and we achieve our results utilizing energy arguments. One of the advantages of our presented method, instead of using plane wave arguments, is that there is no need to make the homogeneous medium assumption to obtain the finite propagation speed results.