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Title: On a class of partial differential equations with nonlocal dirichlet boundary conditions
Authors: Bensoussan, A
Issue Date: 2010
Publisher: Springer
Source: In W Fitzgibbon, Y Kuznetsov, P Neittaanmäki, J Périaux & O Pironneau (Eds.), Applied and numerical partial differential equations : scientific computing in simulation, optimization and control in a multidisciplinary context, p. 9-23. Dordrecht : Springer,: Springer, 2010 How to cite?
Abstract: We establish existence and uniqueness of solutions of a class of partial differential equations with nonlocal Dirchlet conditions in weighted function spaces. The problem is motivated by the study of the probability distribution of the response of an elasto-plastic oscillator when subjected to white noise excitation (see [1,2] on the derivation of the boundary value problem). Note that the developments in [1,2] are based on an extension of Khasminskii's method (see, e.g. [5]) and in this paper we use a direct approach to achieve our objectives. We refer the reader to [3, 4, 6, 7] for general background on modeling, theoretical, and computational issues related to elasto-plastic oscillators.
ISBN: 9789048132393 (electronic bk.)
9789048132386 (print)
DOI: 10.1007/978-90-481-3239-3_3
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