Nonlocal boundary value problems of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

4 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)2783-2805
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume48
Issue number4
Online published30 Aug 2016
Publication statusPublished - 2016

Abstract

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.

Research Area(s)

  • Boundary value problem, Elasto-plastic oscillator, Variational inequality

Citation Format(s)

Nonlocal boundary value problems of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise. / BENSOUSSAN, A.; MERTZ, L.; YAM, S. C. P.
In: SIAM Journal on Mathematical Analysis, Vol. 48, No. 4, 2016, p. 2783-2805.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review