title
  

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

Warning The system is temporarily closed to updates for reporting purpose.

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)

This is the latest version of this item.

[img]PDF - Registered users only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
327Kb

Official URL: http://dx.doi.org/10.1016/j.jde.2020.06.052

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
Uncontrolled Keywords:Viscoelasticity; Strain-limiting theory; Initial-value problem; Local existence
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics
ID Code:41352
Deposited By:Yasemin Şengül Tezel
Deposited On:11 Mar 2021 17:04
Last Modified:11 Mar 2021 17:04

Repository Staff Only: item control page