# Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity

Applications of Mathematics (1992)

- Volume: 37, Issue: 5, page 383-400
- ISSN: 0862-7940

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topŠilhavý, Miroslav. "Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity." Applications of Mathematics 37.5 (1992): 383-400. <http://eudml.org/doc/15723>.

@article{Šilhavý1992,

abstract = {The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions for the corresponding equations.},

author = {Šilhavý, Miroslav},

journal = {Applications of Mathematics},

keywords = {multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry},

language = {eng},

number = {5},

pages = {383-400},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity},

url = {http://eudml.org/doc/15723},

volume = {37},

year = {1992},

}

TY - JOUR

AU - Šilhavý, Miroslav

TI - Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity

JO - Applications of Mathematics

PY - 1992

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 37

IS - 5

SP - 383

EP - 400

AB - The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions for the corresponding equations.

LA - eng

KW - multipolar materials; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry; hereditary laws; Onsager's relations; integral constitutive equations; differential-type viscous materials; thermodynamic compatibility; Onsager-type symmetry

UR - http://eudml.org/doc/15723

ER -

## References

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- J. Nečas A. Novotný, M, Šilhavý, 10.1016/0022-247X(91)90189-7, J. Math. Anal. Appl. 162 (1991), 223-241. (1991) MR1135273DOI10.1016/0022-247X(91)90189-7
- J. Nečas M. Růžička, Global solution to the incompressible viscous-multipolar material, to appear.
- J. Nečas M. Šilhavý, Multipolar viscous fluids, Quart. Appl. Math. 49 (1991), 247-265. (1991) MR1106391
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