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- Title
Exponential Decay for a Time-Varying Coefficients Wave Equation with Dynamic Boundary Conditions.
- Authors
Hao, Jianghao; Du, Fangqing
- Abstract
We consider a wave equation with variable coefficients in time and space in a bounded domain Ω which has the smooth boundary Γ = Γ 0 ∪ Γ 1 such that Γ ¯ 0 ∩ Γ ¯ 1 ≠ ∅ . We study this system that has a homogeneous Dirichlet boundary on Γ 0 and a dynamic boundary on Γ 1 . The innovation of the paper lies in the coefficients which depends on the time variable and the singularities generated by changing the boundary conditions along the interface, thus we need some special techniques to deal with these difficulties. Under some geometric assumptions, the exponential decay result of the system is established by the Riemannian geometry method and the energy perturbation method.
- Publication
Journal of Geometric Analysis, 2024, Vol 34, Issue 5, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-024-01595-9