Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms

Mohammed Aassila

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 223-226
  • ISSN: 0010-2628

Abstract

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In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.

How to cite

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Aassila, Mohammed. "Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 223-226. <http://eudml.org/doc/248417>.

@article{Aassila1999,
abstract = {In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.},
author = {Aassila, Mohammed},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {wave equation; integral inequality; damping and source terms; uniform stabilization; energy decay; exponential decay; initial-boundary value problem; energy decay},
language = {eng},
number = {2},
pages = {223-226},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms},
url = {http://eudml.org/doc/248417},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Aassila, Mohammed
TI - Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 223
EP - 226
AB - In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
LA - eng
KW - wave equation; integral inequality; damping and source terms; uniform stabilization; energy decay; exponential decay; initial-boundary value problem; energy decay
UR - http://eudml.org/doc/248417
ER -

References

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  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. (1991) MR1127082
  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. (1995) Zbl0812.35081MR1306578
  4. Komornik V., Exact Controllability and Stabilization. The Multiplier Method, Masson-John Wiley, Paris, 1994. Zbl0937.93003MR1359765
  5. Lions J.L., Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969. Zbl0248.35001MR0259693
  6. Payne L.E., Sattinger D.H., Saddle points and unstability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303. (1975) MR0402291
  7. Sattinger D.H., On global solution of nonlinear hyperbolic equations, Arch. Rational Mech. Anal. 30 (1968), 148-172. (1968) Zbl0159.39102MR0227616
  8. Tsutsumi M., On solutions of semilinear differential equations in a Hilbert space, Math. Japon. 17 (1972), 173-193. (1972) Zbl0273.34044MR0355247

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