Abstract
Processes governed by Partial Differential Equations (PDE) display very rich dynamical behavior, which is continuous spatially. Influencing the behavior of PDE systems through boundaries is an interesting research as it is involves the handling of infinite dimensionality, due to which the traditional tools of control theory do not apply directly. This study demonstrates how a nonlinear PDE is converted into a reasonably descriptive Ordinary Differential Equation (ODE) model. The approach is based on Proper Orthogonal Decomposition (POD), which separates the temporal and spatial components of the dynamics. The finite term expansion of the solution results in an autonomous ODE and this paper demonstrates how the external excitations are made explicit in the dynamical model. 2D Burgers equation is used to illustrate the effectiveness of the approach and a finite dimensional dynamical model is shown to be capable of capturing the essential response.
This work is supported by TOBB ETÜ BAP Program (Contract No: ETÜ BAP 2006/04)
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Efe, M.Ö. (2007). Modeling of PDE processes with finite dimensional non-autonomous ODE systems. In: Taş, K., Tenreiro Machado, J.A., Baleanu, D. (eds) Mathematical Methods in Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5678-9_14
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DOI: https://doi.org/10.1007/978-1-4020-5678-9_14
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