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Unilateral problems for the wave equation with degenerate and localized nonlinear damping: well‐posedness and non‐stability results
Author(s) -
Cavalcanti A. D. D.,
Cavalcanti M. M.,
Fatori L. H.,
Silva M. A. Jorge
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600413
Subject(s) - degenerate energy levels , mathematics , nonlinear system , stability (learning theory) , zero (linguistics) , manifold (fluid mechanics) , mathematical analysis , riemannian manifold , wave equation , energy (signal processing) , physics , mechanical engineering , linguistics , philosophy , statistics , quantum mechanics , machine learning , computer science , engineering
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.