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An infinite-time relaxation theorem for differential inclusions

Author(s): Brian Ingalls; Eduardo D. Sontag; Yuan Wang
Journal: Proc. Amer. Math. Soc. 131 (2003), 487-499.
MSC (2000): Primary 34A60; Secondary 34D23
Posted: May 22, 2002
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Abstract: The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.

References:

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D. Angeli, B. Ingalls, E. D. Sontag, and Y. Wang, A Relaxation Theorem for Asymptotically Stable Differential Inclusions, in preparation.

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J.-P. Aubin and A. Cellina, Differential Inclusions, Spring-Verlag, Berlin, 1984. MR 85j:49010

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J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990. MR 91d:49001

[4]
R. M. Colombo, A. Fryszkowski, T. Rzezuchowski, and V. Staicu, Continuous Selections of Solution Sets of Lipschitzean Differential Inclusions, Funkcialaj Ekvacioj, 34 (1991), pp. 321-330. MR 93i:34022

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K. Deimling, Multivalued Differential Equations, Walter De Gruyter & Co., Berlin, 1992. MR 94b:34026

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A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic, Dordrecht,

The Netherlands, 1988. MR 90i:34002

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A. Fryszkowski and T. Rzezuchowski, Continuous Version of Filippov-Wazewski Relaxation Theorem, Journal of Differential Equations, 94 (1991), pp. 254-265. MR 92j:34031

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Additional Information:

Brian Ingalls
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
Email: ingalls@math.rutgers.edu

Eduardo D. Sontag
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-\quad 2101
Email: sontag@math.rutgers.edu

Yuan Wang
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991
Email: ywang@math.fau.edu

DOI: 10.1090/S0002-9939-02-06539-5
PII: S 0002-9939(02)06539-5
Received by editor(s): May 28, 2001
Received by editor(s) in revised form: September 19, 2001
Posted: May 22, 2002
Additional Notes: The second author was supported in part by US Air Force Grant F49620-98-1-0242.
The third author's research was supported in part by NSF Grant DMS-9457826.
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2002, American Mathematical Society

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