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Contributions à l'estimation paramétrique des modèles décrits par les équations aux dérivées partielles

Abstract : A large variety of natural, industrial, and environmental systems involves phenomena that are continuous functions not only of time, but also of other independent variables, such as space coordinates. Typical examples are transportation phenomena of mass or energy, such as heat transmission and/or exchange, humidity diffusion or concentration distributions. These systems are intrinsically distributed parameter systems whose description usually requires the introduction of partial differential equations. There is a significant number of phenomena that can be simulated and explained by partial differential equations. Unfortunately all phenomena are not likely to be represented by a single equation. Also, it is necessary to model the largest possible number of behaviors to consider several classes of partial differential equations. The most common are linear equations, but the most representative are non-linear equations. The nonlinear equations can be formulated in many different ways, the interest in nonlinear equations with linear parameters varying is studied. The aim of the thesis is to develop new estimators to identify the systems described by these partial differential equations. These estimators must be adapted with the actual data obtained in experiments. It is therefore necessary to develop estimators that provide convergent estimates when one is in the presence of missing data and are robust to measurement noise. In this thesis, identification methods are proposed for partial differential equation parameter estimation. These methods involve the introduction of estimators based on the instrumental variable technique.
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Contributor : Julien Schorsch <>
Submitted on : Wednesday, December 4, 2013 - 8:50:09 AM
Last modification on : Friday, May 17, 2019 - 11:38:22 AM
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Julien Schorsch. Contributions à l'estimation paramétrique des modèles décrits par les équations aux dérivées partielles. Equations aux dérivées partielles [math.AP]. Université de Lorraine, 2013. Français. ⟨tel-00913579⟩

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