Czasopismo
2009
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Vol. 57, no 1
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25-31
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
A class of infinite-dimensional dissipative dynamical systems is denned 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 → +∞, 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)).
Rocznik
Tom
Strony
25-31
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, U.S.A., ramm@math.ksu.edu
Bibliografia
- [1] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
- [2] A. G. Ramm, Theory and Applications of Some New Classes of Integral Equations, Springer, New York, 1980.
- [3] A. G. Ramm, Stationary regimes in passive nonlinear networks, in: Nonlinear Electromagnetics, P. Uslenghi (ed.), Academic Press, New York, 1980, 263-302.
- [4] A. G. Ramm, Dynamical Systems Method for Solving Operator Equations, Elsevier, Amsterdam, 2007.
- [5] A. G. Ramm, Slow invariant manifolds for dissipative systems, J. Math. Phys. 50 (2009), 042701.
- [6] R. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Amer. Math. Soc., Providence, HI, 1997.
- [7] R. Ternam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0036-0003