An existence result for the fractional Kelvin-Voigt's model on time dependent cracked domains

Abstract
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.
Description
Keywords
linear second order hyperbolic systems, dynamic fracture mechanics, cracking domains, elastodynamics, viscoelasticity, fractional Kelvin-Voigt, Caputo's fractional derivative
Citation
Collections