Exact Null Controllability of a Nonlinear Thermoelastic Contact Problem
- Institute of Mathematics and Mechanics, Russian Academy of Science, Ekaterinburg (Russian Federation) and Department of Science and Mathematics, KetteringUniversity, Flint, MI 48504 (United States), E-mail: isivergi@kettering.edu
- School of Engineering and ComputerScience, Oakland University, Rochester, MI 48309 (United States), E-mail: polis@oakland.edu
We study the controllability properties of a nonlinear parabolic system that models the temperature evolution of a one-dimensional thermoelastic rod that may come into contact with a rigid obstacle. Basically the system dynamics is described by a one-dimensional nonlocal heat equation with a nonlinear and nonlocal boundary condition of Newmann type.We focus on the control problem and treat the case when the control is distributed over the whole space domain. In this case the system is proved to be exactly null controllable provided the parameters of the system are smooth.The proof is based on changing the control variable and using Aubin's Compactness Lemma to obtain an invariant set for the linearized controllability map. Then, by proving that the found solution is sufficiently smooth, we get the null controllability for the original system.
- OSTI ID:
- 21067449
- Journal Information:
- Applied Mathematics and Optimization, Vol. 51, Issue 1; Other Information: DOI: 10.1007/s00245-004-0808-0; Copyright (c) 2005 Springer Science+Business Media, Inc.; Article Copyright (c) 2004 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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