Evolution problems with hysteresis in the source term. (English) Zbl 0618.35053

Visintin, A.

SIAM J. Math. Anal. 17, 1113-1138 (1986).

Author’s abstract. Jump conditions having a hysteresis effect are introduced to model some inertial mechanisms which yield criteria of control of systems. Examples can be found in biology, chemistry, engineering, and economics.
Both orientations of the hysteresis loops are considered, corresponding to ”delay” and ”anticipation” between input and output variables.
Existence results are proved for parabolic and hyperbolic problems and also for the Stefan problem with a term of this type in the second member. A regularizing effect is exhibited by the ”jump with delay” condition.

Reviewer: V.Mustonen

MSC:

35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35R10	Partial functional-differential equations
35R35	Free boundary problems for PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35A15	Variational methods applied to PDEs

Keywords:

Jump conditions; hysteresis effect; control of systems; Existence; Stefan problem; regularizing effect