Unilateral problems for the wave equation with degenerate and localized nonlinear damping: well†posedness and non†stability results

A. D. D. Cavalcanti, M. M. Cavalcanti, L. H. Fatori and M. A. Jorge Silva

Mathematische Nachrichten, 2018, vol. 291, issue 8-9, 1216-1239

Abstract: Unilateral problems related to the wave model subject to degenerate and localized nonlinear damping on a compact Riemannian manifold are considered. Our results are new and concern two main issues: (a) to prove the global well†posedness of the variational problem; (b) to establish that the corresponding energy functional is not (uniformly) stable to equilibrium in general, namely, the energy does not converge to zero on the trajectory of every solution, even if a full linear damping is taken in place.

Date: 2018
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