Attractors of strongly dissipative systems

• Autorzy: Ramm, A. G.
• Języki publikacji: EN

Abstrakty

EN

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)).

Słowa kluczowe

EN

dissipative systems; dynamical systems; attractors; invariant manifolds; nonlinear evolution

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 1
• Strony: 25-31
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Ramm, A. G.

• Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, U.S.A.,

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.