| 摘要: |
| The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion $\omega$ of the domain evolution $\varOmega$. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method (HUM) and Schauder's fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations. |
| 关键词: Distributed systems, fixed point, regional gradient observability, regional reconstruction, semilinear hyperbolic systems |
| DOI： |
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| 基金项目:This work was supported by Academy Hassan II. |
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| Regional gradient observability for semilinear hyperbolic systems: HUM approach |
| A. Khazari,Ali BOUTOULOUT,Imad EL HARRAKI |
| (Sidi Mohamed Ben Abdellah University, \'{E}cole Nationale de Commerce et de gestion, Fez, Morocco;TSI Team, MACS Laboratory, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco;\'{E}cole nationale sup\'{e}rieure des mines de Rabat, Rabat, Morocco) |
| Abstract: |
| The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion $\omega$ of the domain evolution $\varOmega$. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method (HUM) and Schauder's fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations. |
| Key words: Distributed systems, fixed point, regional gradient observability, regional reconstruction, semilinear hyperbolic systems |
