Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Commun. Pure Appl. Anal. |
| Volume: | 20 |
| Number: | 5 |
| Year: | 2021 |
| Pages: | 1931--1960 |
| DOI: | 10.3934/cpaa.2021053 |
| Abstract: | We prove the existence of a unique large-data global-in-time weak solution to a class of models of the form $\bu_{tt} = \mbox{div }\mathbb{T} + \boldf$ for viscoelastic bodies exhibiting strain-limiting behaviour, where the constitutive equation, relating the linearised strain tensor $\beps(\bu)$ to the Cauchy stress tensor $\bbT$, is assumed to be of the form $\beps(\bu_t) + \alpha\beps(\bu) = F(\bbT)$, where we define \( F(\bbT) = ( 1 + |\bbT|^a)^{-\frac{1}{a}}\bbT\), for constant parameters $\alpha \in [0,\infty)$ and $a \in (0,\infty)$, in any number $d$ of space dimensions, with periodic boundary conditions. The Cauchy stress $\bbT$ is shown to belong to $L^{1}(Q)^{d \times d}$ over the space-time domain $Q$. In particular, in three space dimensions, if~$a \in (0,\frac{2}{7})$, then in fact $\bbT \in L^{1+\delta}(Q)^{d \times d}$ for a $\delta > 0$, the value of which depends only on $a$. |
| Preprint project: | NCMM |
| Preprint year: | 2020 |
| Preprint number: | 11 |
| Preprint ID: | NCMM/2020/11 |
| Keywords: | |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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