Non-isothermal viscoelastic flows with conservation laws and relaxation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455586" target="_blank" >RIV/00216208:11320/22:10455586 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=~O6j_CTbuJ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=~O6j_CTbuJ</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219891622500096" target="_blank" >10.1142/S0219891622500096</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-isothermal viscoelastic flows with conservation laws and relaxation

Popis výsledku v původním jazyce

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric energy density (function of the determinant of the deformation gradient detF and the temperature theta like the standard perfect-gas law or Noble-Abel stiffened-gas law) plus a polyconvex strain energy density function of F, theta and of symmetric positive-definite structure tensors that relax at a characteristic time scale. One feature of our model is that it unifies various ideal materials ranging from hyperelastic solids to perfect fluids, encompassing fluids with memory like Maxwell fluids. We establish a strictly convex mathematical entropy to show that the system is symmetric-hyperbolic. Another feature of the proposed model is therefore the short-time existence and uniqueness of smooth solutions, which define genuinely causal viscoelastic flows with waves propagating at finite speed. In heat-conductors, we complement the system by a Maxwell-Cattaneo equation for an energy-flux variable. The system is still symmetric-hyperbolic, and smooth evolutions with finite-speed waves remain well-defined.

Název v anglickém jazyce

Non-isothermal viscoelastic flows with conservation laws and relaxation

Popis výsledku anglicky

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric energy density (function of the determinant of the deformation gradient detF and the temperature theta like the standard perfect-gas law or Noble-Abel stiffened-gas law) plus a polyconvex strain energy density function of F, theta and of symmetric positive-definite structure tensors that relax at a characteristic time scale. One feature of our model is that it unifies various ideal materials ranging from hyperelastic solids to perfect fluids, encompassing fluids with memory like Maxwell fluids. We establish a strictly convex mathematical entropy to show that the system is symmetric-hyperbolic. Another feature of the proposed model is therefore the short-time existence and uniqueness of smooth solutions, which define genuinely causal viscoelastic flows with waves propagating at finite speed. In heat-conductors, we complement the system by a Maxwell-Cattaneo equation for an energy-flux variable. The system is still symmetric-hyperbolic, and smooth evolutions with finite-speed waves remain well-defined.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10102 - Applied 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

Journal of Hyperbolic Differential Equations

ISSN

0219-8916

e-ISSN

1793-6993

Svazek periodika

19

Číslo periodika v rámci svazku

02

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

337-364

Kód UT WoS článku

000840562700005

EID výsledku v databázi Scopus

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