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Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body

Abstract:

We prove the existence of a unique large-data global-in-time weak solution to a class of models of the form utt=div T+f for viscoelastic bodies exhibiting strain-limiting behaviour, where the constitutive equation, relating the linearised strain tensor ε(u) to the Cauchy stress tensor T, is assumed to be of the form ε(ut)+αε(u)=F(T), where we define F(T)=(1+|T|a)−1aT, for constant parameters α∈(0,∞) and a∈(0,∞), in any number d of space dimensions, with periodic boundary conditions. The Cauch...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.3934/cpaa.2021053

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-0812-6105
Publisher:
American Institute of Mathematical Sciences Publisher's website
Journal:
Communications in Pure and Applied Analysis Journal website
Volume:
20
Issue:
5
Pages:
1931-1960
Publication date:
2021-03-22
Acceptance date:
2021-01-04
DOI:
EISSN:
1553-5258
ISSN:
1534-0392
Language:
English
Keywords:
Pubs id:
1152078
Local pid:
pubs:1152078
Deposit date:
2021-01-04

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