Publication database of NCMM , project MORE and MathMAC center.
 [BibTeX] [RIS] [Request]
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 Bulíček, Miroslav
Patel, Victoria
Şengül, Yasemin
Süli, Endre
Added by: [MB]
Total mark: 0
Attachments
  • periodicpaper.pdf
Notes
    Topics