\(n^2\) of dissipative couplings are sufficient to guarantee the exponential decay in elasticity (Q6601250)

In this paper, the authors first proved that, with \(n^2\) dissipation mechanisms and when the rank of the matrix defining the coupling coefficients is maximum, the solutions decay in an exponential way for every (bounded) geometry of the solid, where \(n\) is the dimension of the domain. Also, the authors provide an example when the matrix of coupling terms has rank 2 (in dimension 2) or rank 6 (in dimension 3) such that there are undamped isothermal mechanical oscillations.