Uniform stabilization of a plate equation with nonlinear localized dissipation

Authors

  • Ademir F. Pazoto Universidade Federal do Rio de Janeiro.
  • Lucicléia Coelho Universidade Federal de Santa Catarina.
  • Ruy Coimbra Charao Universidade Federal de Santa Catarina.

DOI:

https://doi.org/10.4067/S0716-09172004000300002

Keywords:

Plate equations, bounded domains, dissipative nonlinear terms, control theory, unique continuation property, Nakao method, uniform stabilization, ecuaciones de placa, dominios acotados, términos disipativos no-lineales, teoría del control.

Abstract

We study the existence and uniqueness of a plate equation in a bounded domain of R?, with a dissipative nonlinear term, localized in a neighborhood of part of the boundary of the domain. We use techniques from control theory, the unique continuation property and Nakao method to prove the uniform stabilization of the energy of the system with algebraic decay rates depending on the order of the nonlinearity of the dissipative term.

Author Biographies

Ademir F. Pazoto, Universidade Federal do Rio de Janeiro.

Instituto de Matemática.

Lucicléia Coelho, Universidade Federal de Santa Catarina.

Departamento de Matemática.

Ruy Coimbra Charao, Universidade Federal de Santa Catarina.

Departamento de Matemática.

References

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Published

2017-05-22

How to Cite

[1]
A. F. Pazoto, L. Coelho, and R. Coimbra Charao, “Uniform stabilization of a plate equation with nonlinear localized dissipation”, Proyecciones (Antofagasta, On line), vol. 23, no. 3, pp. 205-234, May 2017.

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