Geodesic
Energy estimates for solutions of the mixed problem for linear second-order hyperbolic equations
Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 483-488.

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A mixed problem for a linear second-order hyperbolic equation with antidissipation inside the domain and dissipation on a part of the boundary is considered. It is proved that for certain relations between the antidissipation inside the domain and the dissipation on the part of the boundary, the energy of the system exponentially decreases, whereas for sufficiently large antidissipation inside the domain the boundary dissipation has no effect on the energy of the system; in this case the energy remains unbounded. 
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     author = {A. B. Aliev and A. Kh. Khanmamedov},
     title = {Energy estimates for solutions of the mixed problem for linear second-order hyperbolic equations},
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A. B. Aliev; A. Kh. Khanmamedov. Energy estimates for solutions of the mixed problem for linear second-order hyperbolic equations. Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 483-488. http://geodesic.mathdoc.fr/item/MZM_1996_59_4_a0/

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