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

TL;DR

This paper establishes the existence of solutions for a fractional Kelvin-Voigt model on evolving cracked domains, demonstrating energy stability and uniqueness in static crack scenarios.

Contribution

It provides the first existence proof for the fractional Kelvin-Voigt model on time-dependent cracked domains, including regularized solutions and energy inequalities.

Findings

Existence of solutions for the fractional Kelvin-Voigt model on cracked domains.

Solutions satisfy an energy-dissipation inequality.

Uniqueness when the crack remains static.

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.