Exponential decay for semilinear wave equation with localized damping in the hyperbolic space

In this paper, we study the exponential decay of the energy associated to an initial value problem involving the wave equation on the hyperbolic space BN$\mathbb {B}^N$. The space BN$\mathbb {B}^N$ is the unit disc {x∈RN:|x|

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-01, Vol.296 (1), p.130-151
Main Authors: Carrião, Paulo Cesar, Miyagaki, Olímpio Hiroshi, Vicente, André
Format: Article
Language:English
Subjects:
Boundary value problems
Damping
Decay
exponential decay
Hyperbolic coordinates
hyperbolic space
noncompact manifolds
wave equation
Wave equations
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Description
Summary:In this paper, we study the exponential decay of the energy associated to an initial value problem involving the wave equation on the hyperbolic space BN$\mathbb {B}^N$. The space BN$\mathbb {B}^N$ is the unit disc {x∈RN:|x|
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202000083