Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback
- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
The problem of stabilizability from the boundary {partial_derivative}{omega} for a parabolic equation given in a bounded domain {omega} element of R{sup n}, consists in choosing a boundary condition (a control) such that the solution of the resulting mixed boundary-value problem tends as t{yields}{infinity} to a given steady-state solution at a prescribed rate exp(-{sigma}{sub 0}t). Furthermore, it is required that the control be with feedback, that is, that it react to unpredictable fluctuations of the system by suppressing the results of their action on the stabilizable solution. A new mathematical formulation of the concept of feedback is presented and then used in solving the problem of stabilizability of linear as well as quasi-linear parabolic equations by means of a control with feedback defined on part of the boundary.
- OSTI ID:
- 21205593
- Journal Information:
- Sbornik. Mathematics, Vol. 192, Issue 4; Other Information: DOI: 10.1070/SM2001v192n04ABEH000560; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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