Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces

Bachmann, Luisa, De Anna, Francesco, Schlomerkemper, Anja and Şengül, Yasemin 2023. Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 381 (2263) , 20220374. 10.1098/rsta.2022.0374

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Abstract

In this work, we deal with a one-dimensional stress-rate type model for the response of viscoelastic materials, in relation to the strain-limiting theory. The model is based on a constitutive relation of stress-rate type. Unlike classical models in elasticity, the unknown of the model under consideration is uniquely the stress, avoiding the use of the deformation. Here, we treat the case of periodic boundary conditions for a linearized model. We determine an optimal function space that ensures the local existence of solutions to the linearized model around certain steady states. This optimal space is known as the Gevrey-class 3/2, which characterizes the regularity properties of the solutions. The exponent 3/2 in the Gevrey-class reflects the specific dispersion properties of the equation itself. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	The Royal Society
ISSN:	1364-503X
Date of First Compliant Deposit:	20 September 2023
Date of Acceptance:	21 August 2023
Last Modified:	20 Nov 2023 15:02
URI:	https://orca.cardiff.ac.uk/id/eprint/162626

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