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Energy decay for the time dependent damped wave equation (2207.06260v4)
Published 13 Jul 2022 in math.AP, math-ph, math.MP, and math.OC
Abstract: Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions decays at an exponential rate if the damping coefficient satisfies a time dependent analogue of the classical geometric control condition. Existing time dependent observability inequalities are improved by removing technical assumptions on the permitted initial data.