# Remarks on weak stabilization of semilinear wave equations

ESAIM: Control, Optimisation and Calculus of Variations (2001)

- Volume: 6, page 553-560
- ISSN: 1292-8119

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topHaraux, Alain. "Remarks on weak stabilization of semilinear wave equations." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 553-560. <http://eudml.org/doc/90608>.

@article{Haraux2001,

abstract = {If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble.},

author = {Haraux, Alain},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {weak stabilization; semilinear; wave equations; semilinear conservative equation; essentially oscillatory solutions; nonmonotone damping term},

language = {eng},

pages = {553-560},

publisher = {EDP-Sciences},

title = {Remarks on weak stabilization of semilinear wave equations},

url = {http://eudml.org/doc/90608},

volume = {6},

year = {2001},

}

TY - JOUR

AU - Haraux, Alain

TI - Remarks on weak stabilization of semilinear wave equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2001

PB - EDP-Sciences

VL - 6

SP - 553

EP - 560

AB - If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble.

LA - eng

KW - weak stabilization; semilinear; wave equations; semilinear conservative equation; essentially oscillatory solutions; nonmonotone damping term

UR - http://eudml.org/doc/90608

ER -

## References

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