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

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...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022-12, Vol.73 (6), Article 221
Main Authors: Cavalcanti, Marcelo Moreira, Domingos Cavalcanti, Valéria Neves, Vicente, André
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary damping
Coefficients
Dirichlet problem
Engineering
Mathematical Methods in Physics
Smooth boundaries
Stability
Theoretical and Applied Mechanics
Time dependence
Wave equations
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01856-z