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arXiv · 2212.00158

Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach

Ademir F. Pazoto·Miguel Soto
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Abstract

The paper deals with the controllability properties of the Kawahara equation posed on a periodic domain. We show that the equation is exactly controllable by means of a control depending only on time and acting on the system through a given shape function in space. Firstly, the exact controllability property is established for the linearized system through a Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential functions. Finally, the local controllability of the full system is derived by combining the analysis of the linearized system, a fixed point argument and some Bourgain smoothing properties of the Kawahara equation on a periodic domain.

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Ademir F. Pazoto, Miguel Soto. 2022-11-30. Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach. https://arxiv.org/abs/2212.00158

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