Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity

Eduard Feireisl

Aplikace matematiky (1990)

  • Volume: 35, Issue: 3, page 184-191
  • ISSN: 0862-7940

Abstract

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A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of L ∞ - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.

How to cite

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Feireisl, Eduard. "Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity." Aplikace matematiky 35.3 (1990): 184-191. <http://eudml.org/doc/15623>.

@article{Feireisl1990,
abstract = {A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of $L \infty $ - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {invariant region; vanishing viscosity; nonlinear parabolic system; quasilinear one- dimensional telegraph equation; vanishing viscosity; viscosity regularization; quasilinear one- dimensional telegraph equation; generalized invariant regions},
language = {eng},
number = {3},
pages = {184-191},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity},
url = {http://eudml.org/doc/15623},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 3
SP - 184
EP - 191
AB - A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of $L \infty $ - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
LA - eng
KW - invariant region; vanishing viscosity; nonlinear parabolic system; quasilinear one- dimensional telegraph equation; vanishing viscosity; viscosity regularization; quasilinear one- dimensional telegraph equation; generalized invariant regions
UR - http://eudml.org/doc/15623
ER -

References

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  1. K. N. Chueh C. C. Conley J. A. Smoller, Positively invariant regions for systems of non linear diffusion equations, Indiana Univ. Math. J. 26 (1977), 372-7411. (1977) MR0430536
  2. C. M. Dafermos, 10.1137/0518031, SIAM J. Math. Anal. 18 (1987), 409-421. (1987) Zbl0655.35055MR0876280DOI10.1137/0518031
  3. R. J. DiPerna, 10.1007/BF00251724, Arch. Rational Mech. Anal. 82 (1983), 27-70. (1983) Zbl0519.35054MR0684413DOI10.1007/BF00251724
  4. M. Rascle, Un résultat de ,,compacité par compensation à coefficients variables". Application à l'élasticité nonlinéaire, Compt. Rend. Acad. Sci. Paris, Série I, 302 (1986), 311 - 314. (1986) MR0838582
  5. D. Serre, 10.1016/0022-0396(87)90102-1, J. Differential Equations 69 (1987), 46-62. (1987) Zbl0626.35061MR0897440DOI10.1016/0022-0396(87)90102-1
  6. D. Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations a une dimension d'espace, J. Math. pures et appl. 65 (1986), 423 - 468. (1986) MR0881690
  7. T. D. Venttseľ, 10.1007/BF02107558, Soviet Math. J., 31 (1985), 3148- --3153. (1985) DOI10.1007/BF02107558
  8. E. Feireisl, Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations, Apl. mat. 35 (1990), 192-208. (1990) Zbl0737.35040MR1052740

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