| Title:
|
Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
243-255 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B10 |
| MSC:
|
35B45 |
| MSC:
|
35Q20 |
| MSC:
|
35Q72 |
| MSC:
|
73B30 |
| MSC:
|
73D35 |
| MSC:
|
74A15 |
| MSC:
|
74B10 |
| MSC:
|
74B20 |
| idZBL:
|
Zbl 0718.73013 |
| idMR:
|
MR1077895 |
| . |
| Date available:
|
2008-06-05T21:43:40Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106854 |
| . |
| Reference:
|
[1] Dafermos C. M.: Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity.SIAM J. Math. Anal. 13 (1982), 397-408. Zbl 0489.73124, MR 0653464 |
| Reference:
|
[2] Day W. A.: Steady forced vibrations in coupled thermoelasticity.Arch. Rational Mech. Anal. 93 (1986), 323-334. Zbl 0597.73008, MR 0829832 |
| Reference:
|
[3] DiPerna R. J.: Convergence of approximate solutions to conservation laws.Arch. Rational Mech. Anal. 82 (1983), 27-70. Zbl 0519.35054, MR 0684413 |
| Reference:
|
[4] Greenberg J. M., MacCamy R. C., Mizel V. J.: On the existence, uniqueness and stability of solutions of the equation $\rho\chi_{tt} = E(\chi_x)\chi_{xx} + \lambda \chi_{xx}$.J. Math. Mech. 17 (1968), 707-728. MR 0225026 |
| Reference:
|
[5] Kato T.: Locally coercive nonlinear equations, with applications to some periodic solutions.Duke Math. J. 51 (1984), 923-936. Zbl 0571.47051, MR 0771388 |
| Reference:
|
[6] Klainerman S.: Global existence for nonlinear wave equation.Comm. Pure Appl. Math. 33 (1980), 43-101. MR 0544044 |
| Reference:
|
[7] Matsumura A.: Global existence and asymptotics of the solutions of the second order quasilinear hyperbolic equations with the first order dissipation.Publ. Res. Inst. Math. Soc. 13 (1977), 349-379. Zbl 0371.35030, MR 0470507 |
| Reference:
|
[8] Racke R.: Initial boundary value problems in one-dimensional non-linear thermoelasticity.Math. Meth. Appl. Sci. 10 (1988), 517-529. MR 0965419 |
| Reference:
|
[9] Rothe E. H.: Introduction to various aspects of degree theory in Banach spaces.Providence AMS, 1986. Zbl 0597.47040, MR 0852987 |
| Reference:
|
[10] Shibata Y.: On the global existence of classical solutions of mixed problem for some second order nonlinear hyperbolic operators with dissipative term in the interior domain.Funkcialaj Ekvacioj 25 (1982), 303-345. Zbl 0524.35070, MR 0707564 |
| Reference:
|
[11] Slemrod M.: Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity.Arch. Rational Mech. Anal. 76 (1981), 97-134. Zbl 0481.73009, MR 0629700 |
| Reference:
|
[12] Zheng S.: Initial boundary value problems for quasilinear hyperbolic-parabolic coupled systems in higher dimensional spaces.Chinese Ann. of Math. 4B(4) (1983), 443-462. Zbl 0509.35056, MR 0741742 |
| Reference:
|
[13] Zheng S.: Global solutions and applications to a class of quasilinear hyperbolic-parabolic coupled system.Scienta Sinka, Ser. A 27 (1984), 1274-1286. MR 0794293 |
| Reference:
|
[14] Zheng S., Shen W.: Global solutions to the Cauchy problem of quasilinear hyperbolic-parabolic coupled system.Scienta Sinica, Ser. A 10 (1987), 1133-1149. MR 0942420 |
| . |
