Null-controllability for a fourth order parabolic equation under general boundary conditions

Emmanuel Wend-Benedo Zongo; Luc Robbiano

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arXiv · 2309.02181

Null-controllability for a fourth order parabolic equation under general boundary conditions

Emmanuel Wend-Benedo Zongo·Luc Robbiano

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Abstract

In this paper, we consider a fourth order inner-controlled parabolic equation on an open bounded subset of $R^d$, or a smooth compact manifold with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. We derive a spectral inequality for the solution of the parabolic system that yields a null-controllability result. The spectral inequality is a consequence of an interpolation inequality obtained via a Carleman inequality for the bi-Laplace operator under the considered boundary conditions.

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Emmanuel Wend-Benedo Zongo, Luc Robbiano. 2023-09-05. Null-controllability for a fourth order parabolic equation under general boundary conditions. https://arxiv.org/abs/2309.02181

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