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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-11027X" target="_blank" >GX20-11027X: Matematická analýza parciálních diferenciálních rovnic popisujících silně nerovnovážné stavy v otevřených systémech termodynamiky kontinua</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

1095-7154

Svazek periodika

54

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

6186-6222

Kód UT WoS článku

000963562000014

EID výsledku v databázi Scopus

2-s2.0-85139892137