An existence result for the fractional Kelvin-Voigt's model on time dependent cracked domains
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.
linear second order hyperbolic systems, dynamic fracture mechanics, cracking domains, elastodynamics, viscoelasticity, fractional Kelvin-Voigt, Caputo's fractional derivative