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Large time behavior for discontinuous dynamics on Hilbert spaces
Author(s):
Víctor
H.
Cortés;
Humberto
Prado
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1019-1026.
MSC (1991):
Primary 47A40, 47B48, 47A53, 47A58
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Abstract:
This paper is concerned with the behavior in time for a certain class of dynamics which are discontinuous with respect to the time variable. We introduce the corresponding wave operators and we ensure their existence. Moreover, under suitable conditions this class of wave operators can be approximated in the strong sense by a sequence of ordinary wave operators. Our results can be applied to impulsive dynamical systems.
References:
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- D. D. Bainov and N. V. Milev, Stability of linear impulsive differential equations, Int. J. Systems Sci., Vol. 21, 11 (1990), 2217-2224. MR 91k:34067
- 2.
- V. Cortés, C. Fernández, and R. Rebolledo, Wave operators for discontinuous dynamics, submitted.
- 3.
- V. Cortés and H. Prado, Weak scattering and impulsive systems, Preprint.
- 4.
- J. Cook, Cargase Lectures in Theoretical Physics, (F. Lurchit, ed.) Gordon and Breach, New York, 1967.
- 5.
- E. B. Davies, Time dependent scattering theory, Math. Ann. 210 (1974), 149-162. MR 50:1028
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- J. S. Howland, Stationary scattering theory for time dependent Hamiltonian, Math. Ann. 207 (1974), 315-335. MR 49:11284
- 7.
- E. J. P. Schmidt, On scattering by time dependent perturbations, Indiana Univ. Math. J., Vol. 24, 10 (1975), 925-935. MR 52:1360
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Additional Information:
Víctor
H.
Cortés
Affiliation:
Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Anto- fagasta, Chile
Address at time of publication:
Departamento de Matemática y Cs. C., Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Email:
hprado@fermat.usach.cl
Humberto
Prado
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 114-D, Santiago, Chile
DOI:
10.1090/S0002-9939-97-03555-7
PII:
S 0002-9939(97)03555-7
Received by editor(s):
July 14, 1995
Additional Notes:
This research has been partially supported by FONDECYT through grant 1930023, and UCN 40340209
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
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