Non-isothermal viscoelastic flows with conservation laws and relaxation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Non-isothermal viscoelastic flows with conservation laws and relaxation
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
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)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Hyperbolic Differential Equations
ISSN
0219-8916
e-ISSN
1793-6993
Volume of the periodical
19
Issue of the periodical within the volume
02
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
337-364
UT code for WoS article
000840562700005
EID of the result in the Scopus database
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