Mathematics > Analysis of PDEs
[Submitted on 30 Nov 2022
(v1)
, last revised 18 Apr 2023 (this version, v2)]
Title: Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach
Title: 复指数的双正交函数及其在通过矩方法研究Kawahara方程能控性中的应用
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.
Submission history
From: Miguel Soto [view email][v1] Wed, 30 Nov 2022 23:02:29 UTC (13 KB)
[v2] Tue, 18 Apr 2023 21:27:59 UTC (17 KB)
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