Exponential stability for the wave equation with weak nonmonotone damping.
Portugaliae mathematica, Tome 57 (2000) no. 3, pp. 285-310.

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Keywords: semilinear damped wave equation, weak damping, strong asymptotic stability, partition of the domain, rate of growth at infinity, explicit rate of the decay to zero of any solution
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     title = {Exponential stability for the wave equation with weak nonmonotone damping.},
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Martinez, P.; Vancostenoble, J. Exponential stability for the wave equation with weak nonmonotone damping.. Portugaliae mathematica, Tome 57 (2000) no. 3, pp. 285-310. http://geodesic.mathdoc.fr/item/PORMA_2000__57_3_48777/