Attractors of Strongly Dissipative Systems

Volume 57 / 2009

A. G. Ramm Bulletin Polish Acad. Sci. Math. 57 (2009), 25-31 MSC: 37L99, 47H05, 47H20, 47J35, 78A40, 80A30. DOI: 10.4064/ba57-1-3

Abstract

A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as $t\to +\infty$, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).

Authors

  • A. G. RammMathematics Department
    Kansas State University
    Manhattan, KS 66506-2602, U.S.A.
    e-mail

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