TY - JOUR
T1 - Existence and optimal control of mechanical processes with hysteresis in viscous solids
AU - Brokate, M.
AU - Sprekels, J.
N1 - Funding Information:
This work was partially supported by Deutsche Forschungsgemeinschaft, SPP 'Anwendungsbezogene Optimierung und Steuerung'.
PY - 1989
Y1 - 1989
N2 - In this paper, mechanical processes in a viscous one-dimensional solid are considered where a stress-strain relation in the form of a hysteresis loop is assumed. For a certain class of functionals modelling such loops, existence and stability results are established, and the existence of optimal controls for a related control problem is proved. The class of hysteresis functionals considered includes among others the hysteron of the first kind in the sense of Krasnoselskii and the Ishlinskii and Preisach operators.
AB - In this paper, mechanical processes in a viscous one-dimensional solid are considered where a stress-strain relation in the form of a hysteresis loop is assumed. For a certain class of functionals modelling such loops, existence and stability results are established, and the existence of optimal controls for a related control problem is proved. The class of hysteresis functionals considered includes among others the hysteron of the first kind in the sense of Krasnoselskii and the Ishlinskii and Preisach operators.
UR - http://www.scopus.com/inward/record.url?scp=0024882228&partnerID=8YFLogxK
U2 - 10.1093/imamat/43.3.219
DO - 10.1093/imamat/43.3.219
M3 - Article
AN - SCOPUS:0024882228
SN - 0272-4960
VL - 43
SP - 219
EP - 229
JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
IS - 3
ER -