On a Kelvin-Voigt Viscoelastic Wave Equation with Strong Delay
| Autor: | Anikushyn, Andrii, Demchenko, Anna, Pokojovy, Michael |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized 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 $C^{0}$- 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 $\tau \to 0$ is further studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented. Comment: 34 pages, 4 figures, 1 set of Matlab codes |
| Databáze: | arXiv |
| Externí odkaz: |
|