# Remarks on weak stabilization of semilinear wave equations

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 553-560. <http://eudml.org/doc/197309>.

@article{Haraux2010,

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},

month = {3},

pages = {553-560},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/197309},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Haraux, Alain

TI - Remarks on weak stabilization of semilinear wave equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

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/197309

ER -

## References

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