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

作者：Cavalcanti A D D; Cavalcanti M M; Fatori L H; Jorge Silva M A

来源：Mathematische Nachrichten, 2018, 291(8-9): 1216-1239.

DOI：10.1002/mana.201600413

• non-stability
• obstacle problem
• Riemannian manifold
• spatial-time degenerate damping
• wave equation

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.

• 出版日期2018-6