Wave equations on compact curved spaces admit finite-dimensional global attractors when the damping acts only on an epsilon-controllable region whose interior and boundary measures are arbitrarily small.
Burq, Contrˆ olabilit´ e exacte des ondes dans des ouverts peu r´ eguliers, Asymptot
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Dynamics of Riemann waves with sharp measure-controlled damping
Wave equations on compact curved spaces admit finite-dimensional global attractors when the damping acts only on an epsilon-controllable region whose interior and boundary measures are arbitrarily small.