$$n^2$$ of dissipative couplings are sufficient to guarantee the exponential decay in elasticity
José R. Fernández, Ramón Quintanilla · Ricerche di Matematica · 2022
Abstract In this paper, we prove that the solutions to the problem determined by an elastic material with $$n^2$$ n 2 coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than $$n^2$$ n 2 (2 in dimension 2 and 6 in dimension 3).