Abstract
Our purpose is to provide, in this chapter, the introductory framework to the topics to be dealt with through the rest of this textbook. We will thus present some mathematical methods suitable for the analysis of nonlinear stochastic systems which are modelled by stochastic and random nonlinear partial differential equations. These methods will be developed with particular attention to their applications to the physics of continuum and to mechanics. In this respect, a partial differential equation can, in many cases, be regarded as a mathematical model of a real physical system, which governs the time and/or space evolution of its dependent variables. As such, the model equation describes the physical state of the system. When the state of the system is defined by more than one variable, the mathematical model is given in terms of a set of equations, the number of which is equal to the number of components of the state variable.
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References to Chapter 1
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© 1992 Springer Science+Business Media Dordrecht
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Bellomo, N., Brzezniak, Z., de Socio, L.M. (1992). Stochastic Models and Random Evolution Equations. In: Nonlinear Stochastic Evolution Problems in Applied Sciences. Mathematics and Its Applications, vol 82. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1820-0_1
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DOI: https://doi.org/10.1007/978-94-011-1820-0_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4803-3
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