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Stability for a nonlinear hyperbolic equation with time-dependent coefficients and boundary damping.

Authors :
Cavalcanti, Marcelo Moreira
Domingos Cavalcanti, Valéria Neves
Vicente, André
Source :
Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Dec2022, Vol. 73 Issue 6, p1-20. 20p.
Publication Year :
2022

Abstract

In this paper, we prove a stability result for a nonlinear wave equation, defined in a bounded domain of R N , N ≥ 2 , with time-dependent coefficients. The smooth boundary of Ω is Γ = Γ 0 ∪ Γ 1 such that Σ = Γ ¯ 0 ∩ Γ ¯ 1 ≠ ∅ . On Γ 0 we consider the homogeneous Dirichlet boundary condition and on Γ 1 we consider the Neumann boundary condition with damping term. The presence of time-dependent coefficients and, moreover, of the singularities generated by the condition Σ ≠ ∅ brings some technical difficulties. The tools are the combination of appropriate functional with the techniques due to Bey, Loheac, and Moussaoui [2] and new technical arguments. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00442275
Volume :
73
Issue :
6
Database :
Academic Search Index
Journal :
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Publication Type :
Academic Journal
Accession number :
160255082
Full Text :
https://doi.org/10.1007/s00033-022-01856-z