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Exact Finite Dimensional Feedback Control via Inertial Manifold Theory with Application to the Chafee–Infante Equation

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Abstract

A class of nonlinear parabolic partial differential equations is considered, and an exact finite dimensional feedback control law is designed in order to force the systems to behave in a prescribed way. The feedback law is obtained via inertial manifold theory by reducing the system to finite dimensions. The control achieved is exact, as opposed to approximate, as obtained in a previous work. The result is applied to the Chafee–Infante equation, a one-dimensional scalar reaction-diffusion equation, with distributed control.

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  1. Departamento de Matemática Aplicada, IM-UFRJ, Caixa Postal 68530, Rio de Janeiro, RJ, C.E.P, 21945-970, Brazil

    Ricardo Rosa

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Rosa, R. Exact Finite Dimensional Feedback Control via Inertial Manifold Theory with Application to the Chafee–Infante Equation. Journal of Dynamics and Differential Equations 15, 61–86 (2003). https://doi.org/10.1023/A:1026153311546

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