In this paper, we prove the diffusion phenomenon for the linear wave equation with space-dependent damping. We prove that the asymptotic profile of the solution is given by a solution of the corresponding heat equation in the $L^2$-sense.
Event-triggered damping stabilization of a linear wave equation
Event-triggering mechanism to damp the linear wave equation
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with $L^r$-data
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