Stabilization of elastic plates with variable coefficients and dynamical boundary control
Authors:
Yuxia Guo, Shugen Chai and Pengfei Yao
Journal:
Quart. Appl. Math. 60 (2002), 383-400
MSC:
Primary 93D15; Secondary 74K20, 74M05, 93C20
DOI:
https://doi.org/10.1090/qam/1900498
MathSciNet review:
MR1900498
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Abstract: The aim of this paper is to investigate the stabilization of a hybrid system composed of a plate equation with variable coefficients and two ordinary differential equations under some suitable feedbacks. A rational energy decay rate is established by the multiplier method and the Riemannian geometry method, and the uniform energy decay rate for a simplified system is obtained.
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B. Rao, Stabilization of elastic plate with dynamical boundary control, SIAM J. Control Optim. 36, 148–163 (1998)
P. F. Yao, On the observability inequality for exact controllability of wave equations with variable coefficients, SIAM J. Control Optim. 37, 1568–1599 (1999)
E. Hebey, Sobolev Spaces on Riemannian Manifolds, Lecture Notes in Mathematics, 1635, Springer-Verlag, Berlin, Heidelberg, 1996
M. E. Taylor, Partial Differential Equations I, Springer-Verlag, New York, 1996
H. Wu, C. L. Shen, and Y. L. Yu, An Introduction to Riemannian Geometry (in Chinese), Univ. of Beijing, 1989
P. F. Yao, On the shallow shell equations, to appear
P. F. Yao, Observability inequalities for the Euler-Bernoulli plate with variable coefficients, Contemporary Mathematics 268, 383–406 (2000)
P. F. Yao, Observability inequalities for shallow shells, SIAM J. Control Optim. 38, 1729–1756 (2000)
B. Rao, Stabilization of Kirchhoff plate equation in star-shaped domain by nonlinear boundary feedback, Nonlinear Anal. 20, 605–626 (1993)
V. Komornik, Exact controllability and stabilization, The multiplier method, Masson, Paris, 1994
J. E. Lagnese, Boundary stabilization of thin plates, SIAM, Philadelphia, PA, 1989
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983
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© Copyright 2002
American Mathematical Society
