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The Null Boundary Controllability for a Fourth-Order Parabolic Equation with Samarskii–Ionkin-Type Boundary Conditions

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Abstract

This paper presents a moment method approach to solve the null boundary controllability problem for a fourth-order parabolic equation subject to Samarskii–Ionkin-type boundary conditions. The problem is solved in two stages. First, we demonstrate that the eigenfunctions of the system, which are not self-adjoint under these boundary conditions, form a Riesz basis in \(L_2\) space. Using Fourier’s method, we construct a biorthonormal system of functions to express the series solution. In the second stage, we use these spectral results to show that the system is null boundary controllable for a specific class of initial data. Our approach extends the existing literature on null boundary controllability of parabolic equations and provides new insights into the properties of systems subject to Samarskii–Ionkin-type boundary conditions.

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  1. Department of Mathematics in Faculty of Science, Gebze Technical University, 41100, Kocaeli, Turkey

    Isil Oner

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Oner, I. The Null Boundary Controllability for a Fourth-Order Parabolic Equation with Samarskii–Ionkin-Type Boundary Conditions. Mediterr. J. Math. 20, 323 (2023). https://doi.org/10.1007/s00009-023-02525-9

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  • DOI: https://doi.org/10.1007/s00009-023-02525-9

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