Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity

Erbay, Hüsnü Ata and Erkip, Albert and Şengül Tezel, Yasemin (2020) Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity. Journal of Differential Equations, 269 (11). pp. 9720-9739. ISSN 0022-0396 (Print) 1090-2732 (Online) Published Online First http://dx.doi.org/10.1016/j.jde.2020.06.052

Warning
There is a more recent version of this item available.
Full text not available from this repository. (Request a copy)

Abstract

In this work we prove local existence of strong solutions to the initial-value prob- lem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the strain variable. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.
Item Type: Article
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Yasemin Şengül Tezel
Date Deposited: 09 Jul 2020 13:34
Last Modified: 11 Mar 2021 17:04
URI: https://research.sabanciuniv.edu/id/eprint/40010

Available Versions of this Item

Actions (login required)

View Item
View Item