Inserted: 4 nov 2020
Last Updated: 2 sep 2021
Journal: Journal of Evolution Equations
We prove an existence result for the fractional Kelvin–Voigt’s model involving Caputo’s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt’s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.
Keywords: Viscoelasticity, linear second order hyperbolic systems, dynamic fracture mechanics, cracking domains, fractional Kelvin-Voigt, Caputo's fractional derivative