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Exact null controllability of KdV-Burgers equation with memory effect systems. (English) Zbl 1256.49008
Summary: This paper is concerned with exact null controllability analysis of the nonlinear KdV-Burgers equation with memory. The proposed approach relies upon regression tools to prove the controllability property of the linearized KdV-Burgers equation via Carleman estimates. The control is distributed along with subdomain $\omega \subset \Omega$ and the external control acts on the key role of observability inequality with memory. This description finally shows the exact null controllability guaranteeing the stability.

MSC:
49J20Optimal control problems with PDE (existence)
35Q53KdV-like (Korteweg-de Vries) equations
93B05Controllability
93D20Asymptotic stability of control systems
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