On weak solutions to a viscoelasticity model

Jaroslav Milota; Jindřich Nečas; Vladimír Šverák

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 3, page 557-565
  • ISSN: 0010-2628

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Milota, Jaroslav, Nečas, Jindřich, and Šverák, Vladimír. "On weak solutions to a viscoelasticity model." Commentationes Mathematicae Universitatis Carolinae 031.3 (1990): 557-565. <http://eudml.org/doc/17877>.

@article{Milota1990,
author = {Milota, Jaroslav, Nečas, Jindřich, Šverák, Vladimír},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear memory response; kernel with special properties; global existence; a priori estimates; compact embedding; viscoelastic materials of integral type; existence of global in time weak solutions; Galerkin method; method of monotone operators; convergence},
language = {eng},
number = {3},
pages = {557-565},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On weak solutions to a viscoelasticity model},
url = {http://eudml.org/doc/17877},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Milota, Jaroslav
AU - Nečas, Jindřich
AU - Šverák, Vladimír
TI - On weak solutions to a viscoelasticity model
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 3
SP - 557
EP - 565
LA - eng
KW - linear memory response; kernel with special properties; global existence; a priori estimates; compact embedding; viscoelastic materials of integral type; existence of global in time weak solutions; Galerkin method; method of monotone operators; convergence
UR - http://eudml.org/doc/17877
ER -

References

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  2. Coleman B. D., Noll W., An approximation theorem for functionals with applications in continuum mechanics, Arch. Rat. Mech. Anal. 6 (I960), 355-370. Zbl0097.16403MR0119598
  3. Engler H., Weak solutions of a class of quasilinear hyperbolic integro-differential equations describing viscoelastic materials, (preprint). Zbl0832.45009MR1079180
  4. Lions J. L., Quelques methodes de resolution problemes aux limites non lineaires, Dunod, Paris, 1969. (1969) MR0259693
  5. Lions J. L., Magenes E., Problemes aux limiies non homogenes et applications, Vol I, Dunod, Paris, 1968. (1968) 
  6. Londen S. O., An existence result on a Volterra equation in a Banach space, TAMS 235 (1978), 285-304. (1978) Zbl0376.45011MR0473770
  7. Miller R. K., Nonlinear Volterra Integral Equations, Benjamin, 1971. (1971) Zbl0448.45004MR0511193
  8. Minty G., Monotone (nonlinear) operators in a Hilbert space, Duke Math. J. 29 (1962), 341-348. (1962) MR0169064
  9. Nohel J. A., Rogers R. C., Tzavaras A. E., Weak solutions for a nonlinear system in viscoelasticity, Coram. Part. Diff. Eqs. 13 (1988), 97-127. (1988) Zbl0635.73047MR0914816
  10. Renardy M., Hrusa M. J., Nohel J. A., Mathematical problems in viscoelasticity, Longman, 1987. (1987) Zbl0719.73013
  11. Saut J. C., Joseph D. D., Fading memory, Arch. Rat. Mech. Anal. 81 (1982), 53-95. (1982) MR0679915

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