A Probabilistic Multiscale Approach to Hysteresis in Shear Wave Propagation in Biotissue
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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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.
- Genetic Engineering and Molecular Biology
- Statistics and Probability
- Medicine and Medical Research
- Numerical Mathematics