| Title:
|
Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms (English) |
| Author:
|
Aassila, Mohammed |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
223-226 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms. (English) |
| Keyword:
|
wave equation |
| Keyword:
|
integral inequality |
| Keyword:
|
damping and source terms |
| Keyword:
|
uniform stabilization |
| Keyword:
|
energy decay |
| MSC:
|
35B40 |
| MSC:
|
35L70 |
| idZBL:
|
Zbl 0977.35025 |
| idMR:
|
MR1732643 |
| . |
| Date available:
|
2009-01-08T18:51:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119078 |
| . |
| Reference:
|
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| Reference:
|
[2] Hosoya M., Yamada Y.: On some nonlinear wave equations 2: global existence and energy decay of solutions.J. Fac. Sci. Univ. Tokyo Sect.IA, Math. 38 (1991), 239-250. MR 1127082 |
| Reference:
|
[3] Ikehata R.: A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms.Differential and Integral Equations 8(3) (1995), 607-616. Zbl 0812.35081, MR 1306578 |
| Reference:
|
[4] Komornik V.: Exact Controllability and Stabilization. The Multiplier Method.Masson-John Wiley, Paris, 1994. Zbl 0937.93003, MR 1359765 |
| Reference:
|
[5] Lions J.L.: Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires.Dunod, Paris, 1969. Zbl 0248.35001, MR 0259693 |
| Reference:
|
[6] Payne L.E., Sattinger D.H.: Saddle points and unstability of nonlinear hyperbolic equations.Israel J. Math. 22 (1975), 273-303. MR 0402291 |
| Reference:
|
[7] Sattinger D.H.: On global solution of nonlinear hyperbolic equations.Arch. Rational Mech. Anal. 30 (1968), 148-172. Zbl 0159.39102, MR 0227616 |
| Reference:
|
[8] Tsutsumi M.: On solutions of semilinear differential equations in a Hilbert space.Math. Japon. 17 (1972), 173-193. Zbl 0273.34044, MR 0355247 |
| . |
