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Asymptotic stability for nonlinear PDEs with hysteresis

Published online by Cambridge University Press:  26 September 2008

Nobuyuki Kenmochi  and
Augusto Visintin
Nobuyuki Kenmochi
Affiliation:
Department of Mathematics, Faculty of Education, Chiba University, 1–33 Yayoi-chō, Chiba, 260Japan
Augusto Visintin
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy
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Abstract

Nonlinear evolution equations including hysteresis functionals are studied. It is the purpose of this paper to investigate the asymptotic stability of the solution as time t → + ∞. In the case when the forcing term of the equation tends to a time-independent function as t → + ∞, we shall show that the solution stabilizes at + ∞ and the system is asymptotically stable (equilibrium stability). In the case when the forcing term is periodic in time, we shall show that there is at least one periodic solution and that in some restricted cases the periodic solution is unique.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 1 , March 1994 , pp. 39 - 56
Copyright
Copyright © Cambridge University Press 1994

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