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

Erbay, H. A., Erkip, A. and Sengul, Y. 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. 10.1016/j.jde.2020.06.052

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Abstract

In this work we prove local existence of strong solutions to the initial-value problem 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. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. 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 sum of the strain and the strain rate. 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
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0022-0396
Date of Acceptance: 18 June 2020
Last Modified: 15 Nov 2021 13:50
URI: https://orca.cardiff.ac.uk/id/eprint/145142

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