Unique Continuation, Uniqueness and Optimization for Biomechanical Imaging Viscoelastic Models

Tuesday, February 14, 2017 - 9:00am - 9:50am
Keller 3-180
Joyce Mclaughlin (Rensselaer Polytechnic Institute)
In biomechanical Imaging of tissue and in geophysics, viscoelastic models are used in order for the mathematical models: (1) to accurately predict the data; and (2) given the data, to enable the imaging functional to accurately compute biomechanical properties of tissue or physical properties of the earth. The mathematical structure of these integro-differential operators, in the time/space domain, have new properties. We present unique continuation results which will be used to establish uniqueness results in the time/space domain for biomechanical imaging; we also present optimization results to recover hydrostatic pressure and the shear modulus in the frequency domain with the aim to apply the results to biomechanical imaging,