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@ARTICLE{,
            author = {Bul{\'{\i}}{\v c}ek, Miroslav and Patel, Victoria and Şeng{\"{u}}l, Yasemin and S{\"{u}}li, Endre},
             title = {Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body},
           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}
}