Work

On a Kelvin-Voigt Viscoelastic Wave Equation with Strong Delay

Year: 2018

Type: book

Abstract: An initial-boundary value problem for a viscoelastic wave equation subject to a strong timelocalized delay in a Kelvin & Voigt-type material law is considered. Transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued C0- and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using the Lyapunov’s indirect method. The singular limit τ -> 0 is further studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.

Source: Repository KITopen (Karlsruhe Institute of Technology)

DOI: 10.48550/arxiv.1810.02931

Authors: Anikushyn, Andrii, Demchenko, Anna, Pokojovy, Michael

Institutions: Taras Shevchenko National University of Kyiv, Masaryk University, The University of Texas at El Paso

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, University of Texas at El Paso, Erasmus+

Award: G5752180124