Inertial Manifolds for von Karman Plate Equations
- Department of Mathematics and Mechanics, Kharkov University, Kharkov 310077 (Ukraine), E-mail: chueshov@univer.kharkov.ua
- Department of Mathematics, University of Virginia, Charlottesville, VA 22903 (United States), E-mail: il2v@virginia.edu
Inertial manifolds associated with nonlinear plate models governed by dynamical von Karman equations are considered. Three different dissipative mechanisms are discussed: viscous, structural and thermal damping. Though the systems considered are subject to some dissipation, the overall dynamics may not be dissipative. This means that the energy may not be decreasing. The main result of the paper establishes the existence of an inertial manifold subject to the spectral gap condition for linearized problems. The validity of the spectral gap condition depends on the geometry of the domain and the type of damping. It is shown that the spectral gap condition holds for plates of rectangular shape. In the case of viscous damping, which is associated with hyperbolic-like dynamics, it is also required that the damping parameter be sufficiently large. This last requirement is not needed for other types of dissipation considered in the paper.
- OSTI ID:
- 21064246
- Journal Information:
- Applied Mathematics and Optimization, Vol. 46, Issue 2-3; Other Information: DOI: 10.1007/s00245-002-0741-7; Copyright (c) 2002 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 2002 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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