Abstract
We prove the existence and uniqueness of strong and weak solutions as well as the uniform stabilization of the energy of initial boundary value problem for a hyperbolic equation in a class of domains Ω ⊂ \( \Omega \subset \mathbb{R}^N \) which includes simply connected regions. The boundary Γ of Ω can be a smooth simple connected manifold and the boundary conditions are acoustic boundary conditions on a portion Γ1 of the boundary and the Dirichlet boundary condition on the rest of Γ.
Partially supported by research grant from CNPq-Brazil.
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Dedicated to Professor Djairo Guedes de Figueiredo on the occasion of his 70th birthday
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Frota, C.L., Larkin, N.A. (2005). Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains. In: Cazenave, T., et al. Contributions to Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 66. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7401-2_20
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DOI: https://doi.org/10.1007/3-7643-7401-2_20
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