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math.AP2021★ 16 cited
Determining kernels in linear viscoelasticity
Barbara Kaltenbacher, Ustim Khristenko, Vanja Nikolić +2
In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal vi…
math.AP2021★ 25 cited
Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
Marvin Fritz, Ustim Khristenko, Barbara Wohlmuth
Time-fractional partial differential equations are nonlocal in time and show an innate memory effect. In this work, we propose an augmented energy functional which includes the his…