| Title:
|
Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1990 |
| Pages:
|
184-191 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
invariant region |
| Keyword:
|
vanishing viscosity |
| Keyword:
|
nonlinear parabolic system |
| Keyword:
|
quasilinear one- dimensional telegraph equation |
| MSC:
|
35B35 |
| MSC:
|
35B45 |
| MSC:
|
35B65 |
| MSC:
|
35K45 |
| MSC:
|
35K55 |
| MSC:
|
73C50 |
| MSC:
|
73D35 |
| MSC:
|
74B20 |
| idZBL:
|
Zbl 0709.73013 |
| idMR:
|
MR1052739 |
| DOI:
|
10.21136/AM.1990.104402 |
| . |
| Date available:
|
2008-05-20T18:39:07Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104402 |
| . |
| Reference:
|
[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. MR 0430536 |
| Reference:
|
[2] C. M. Dafermos: Estimates for conservation laws with little viscosity.SIAM J. Math. Anal. 18 (1987), 409-421. Zbl 0655.35055, MR 0876280, 10.1137/0518031 |
| Reference:
|
[3] R. J. DiPerna: Convergence of approximate solutions to conservation laws.Arch. Rational Mech. Anal. 82 (1983), 27-70. Zbl 0519.35054, MR 0684413, 10.1007/BF00251724 |
| Reference:
|
[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. MR 0838582 |
| Reference:
|
[5] D. Serre: Domaines invariants pour les systèmes hyperboliques de lois de conservation.J. Differential Equations 69 (1987), 46-62. Zbl 0626.35061, MR 0897440, 10.1016/0022-0396(87)90102-1 |
| Reference:
|
[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. MR 0881690 |
| Reference:
|
[7] T. D. Venttseľ: Estimates of solutions of the one-dimensional system of equations of gas dynamics with "viscosity" nondepending on "viscosity".Soviet Math. J., 31 (1985), 3148- --3153. 10.1007/BF02107558 |
| Reference:
|
[8] E. Feireisl: Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations.Apl. mat. 35 (1990), 192-208. Zbl 0737.35040, MR 1052740 |
| . |
