TY - JOUR
T1 - Nonlocal boundary value problems of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise
AU - BENSOUSSAN, A.
AU - MERTZ, L.
AU - YAM, S. C. P.
PY - 2016
Y1 - 2016
N2 - In the literature, failure risk analysis on most elasto-perfectly-plastic oscillators is essentially focused on those excited by white noise, which is rather restrictive from the modeling perspective. Our present article is motivated by the study of the probability distribution of the solution of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise. We introduce a class of partial differential equations (PDEs) with nonlocal Dirichlet conditions and we establish the unique existence of solutions of these PDEs by extending the method developed in [A. Bensoussan and J. Turi, Applied and Numerical Partial Differential Equations, Comput. Methods Appl. Sci. 15, Springer, New York, 2009, pp. 9-23]. A major mathematical challenge here is to carry out the analysis of boundary value problems for elliptic equations in dimension two rather than that in dimension one.
AB - In the literature, failure risk analysis on most elasto-perfectly-plastic oscillators is essentially focused on those excited by white noise, which is rather restrictive from the modeling perspective. Our present article is motivated by the study of the probability distribution of the solution of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise. We introduce a class of partial differential equations (PDEs) with nonlocal Dirichlet conditions and we establish the unique existence of solutions of these PDEs by extending the method developed in [A. Bensoussan and J. Turi, Applied and Numerical Partial Differential Equations, Comput. Methods Appl. Sci. 15, Springer, New York, 2009, pp. 9-23]. A major mathematical challenge here is to carry out the analysis of boundary value problems for elliptic equations in dimension two rather than that in dimension one.
KW - Boundary value problem
KW - Elasto-plastic oscillator
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=84984950119&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84984950119&origin=recordpage
U2 - 10.1137/16M1056237
DO - 10.1137/16M1056237
M3 - RGC 21 - Publication in refereed journal
VL - 48
SP - 2783
EP - 2805
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 4
ER -