Calculus of Variations and Geometric Measure Theory

M. Caponi - F. Sapio

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

created by caponi on 04 Nov 2020
modified by sapio on 02 Sep 2021


Published Paper

Inserted: 4 nov 2020
Last Updated: 2 sep 2021

Journal: Journal of Evolution Equations
Year: 2021

ArXiv: 2011.02214 PDF
Links: Journal site


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