EXISTENCE AND UNIQUENESS OF GLOBAL WEAK SOLUTIONS TO STRAIN-LIMITING VISCOELASTICITY WITH DIRICHLET BOUNDARY DATA

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452925" target="_blank" >RIV/00216208:11320/22:10452925 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=oOijdcdmC8" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=oOijdcdmC8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1455322" target="_blank" >10.1137/21M1455322</a>

Result language
angličtina
Original language name
EXISTENCE AND UNIQUENESS OF GLOBAL WEAK SOLUTIONS TO STRAIN-LIMITING VISCOELASTICITY WITH DIRICHLET BOUNDARY DATA
Original language description
We consider a system of evolutionary equations that is capable of describing certain viscoelastic effects in linearized yet nonlinear models of solid mechanics. The constitutive relation, involving the Cauchy stress, the small strain tensor, and the symmetric velocity gradient, is given in an implicit form. For a large class of these implicit constitutive relations, we establish the existence and uniqueness of a global-in-time large-data weak solution. Then we focus on the class of so-called limiting strain models, i.e., models for which the magnitude of the strain tensor is known to remain small a priori, regardless of the magnitude of the Cauchy stress tensor. For this class of models, a new technical difficulty arises. The Cauchy stress is only an integrable function over its domain of definition, resulting in the underlying function spaces being nonreflexive and thus the weak compactness of bounded sequences of elements of these spaces is lost. Nevertheless, even for problems of this type we are able to provide a satisfactory existence theory, as long as the initial data have finite elastic energy and the boundary data fulfill natural compatibility conditions.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-11027X" target="_blank" >GX20-11027X: Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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