Artículo
Dynamics of Riemann waves with sharp measure-controlled damping
Autor/es | Cavalcanti, M.M.
Ma, To Fu Marín Rubio, Pedro Seminario Huertas, Paulo Nicanor |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2019-08-13 |
Fecha de depósito | 2023-01-31 |
Publicado en |
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Resumen | This paper is concerned with locally damped semilinear wave equations
defined on compact Riemannian manifolds with boundary. We present a
construction of measure-controlled damping regions which are sharp in the
sense ... This paper is concerned with locally damped semilinear wave equations defined on compact Riemannian manifolds with boundary. We present a construction of measure-controlled damping regions which are sharp in the sense that their summed interior and boundary measures are arbitrarily small. The construction of this class of open sets is purely geometric and allows us to prove a new observability inequality in terms of potential en ergy rather than the usual one with kinetic energy. A unique continuation property is also proved. Then, in three-dimension spaces, we establish the existence of finite dimensional smooth global attractors for a class of wave equations with nonlinear damping and C 1 -forces with critical Sobolev growth. In addition, by means of an obstacle control condition, we show that our class of measure-controlled regions satisfies the well-known geo metric control condition (GCC). Therefore, many of known results for the stabilization of wave equations hold true in the present context. |
Cita | Cavalcanti, M.M., Ma, T.F., Marín Rubio, P. y Seminario Huertas, P.N. (2019). Dynamics of Riemann waves with sharp measure-controlled damping. https://doi.org/10.48550/arXiv.1908.04814. |
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