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Uniqueness theorem for a Cauchy problem with hysteresis
Author(s):
Jana
Kopfová
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3527-3532.
MSC (1991):
Primary 34A12;
Secondary 34A60
Posted:
August 5, 1999
MathSciNet review:
1694870
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Abstract:
The Cauchy problem for an ordinary differential equation coupled with a hysteresis operator is studied. Under physically reasonable assumptions on the forcing term, uniqueness of solutions is shown without assuming Lipschitz continuity of the hysteresis curves. The result is true for any kind of hysteresis operators with monotone curves of motion.
References:
- 1.
- V.Chernorutskii and D.Rachinskii, On uniqueness of an initial-value problem for ODE with hysteresis, Nonl. Diff. Equ. Appl. 4, 1997, 391-399. MR 98j:34004
- 2.
- P.Hartman, Ordinary Differential Equations, Birkhäuser, 1982. MR 83e:34002
- 3.
- M.A.Krasnosel'skii and A.V.Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. MR 90a:93001
- 4.
- A.Visintin, Differential Models of Hysteresis, Springer-Verlag, Berlin, 1995. MR 96h:47001
- 5.
- A.A.Vladimirov, M.A.Krasnosel'skii, and V.V.Chernorutskii, The Cauchy problem for systems with hysteresis, Russian Acad. Sci. Dokl. Math. 48 (1994), 502-506. MR 94k:47104
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Additional Information:
Jana
Kopfová
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Address at time of publication:
Slezska Univerzita, Matematicky ustav, Bezrucovo nam. 13, 746 01 Opava, Czech Republic
Email:
kopf@phys.ualberta.ca, jana.kopfova@math.slu.cz
DOI:
10.1090/S0002-9939-99-05531-8
PII:
S 0002-9939(99)05531-8
Received by editor(s):
October 11, 1996
Posted:
August 5, 1999
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1999,
American Mathematical Society
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