A Probabilistic Multiscale Approach to Hysteresis in Shear Wave Propagation in Biotissue

Abstract

Motivated by a problem involving wave propagation through viscoelastic biotissue, we present a theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables. The resulting systems entail probability measure-dependent partial differential equations for which we establish well-posedness in a framework that leads readily to computationally useful approximations.