Uniform exponential stability and approximation in control of a thermoelastic system. (English) Zbl 0815.93040
Summary: This paper has two objectives. First, necessary and sufficient conditions are given to characterize the uniform exponential stability of a sequence of \(c_ 0\)-semigroups \(T_ n (t)\) on Hilbert space \(H_ n\). Secondly, approximation in control of a one-dimensional thermoelastic system, subject to Dirichlet-Dirichlet as well as Dirichlet-Neumann boundary conditions, is considered. The uniform exponential stability and strong convergence of corresponding semigroups associated with approximate scheme are proved. Numerical experimental results are also presented.
MSC:
93C20 | Control/observation systems governed by partial differential equations |
93D20 | Asymptotic stability in control theory |
74B99 | Elastic materials |
74H99 | Dynamical problems in solid mechanics |
41A10 | Approximation by polynomials |
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |