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<p>This paper deals with the Neumann boundary controllability of a system of Petrovsky-Petrovsky type which is coupled through the velocities. We are interested in controlling the corresponding state which has two components by exerting only one boundary control force on the system. We prove that, under the usual multiplier geometric control condition and for small coupling coefficient <i>b</i>, there exists a time <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_710_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_b&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mi>b</mi> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> such that the system is null controllable at any time <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_710_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(T&gt; T_b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>&gt;</mo> <msub> <mi>T</mi> <mi>b</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. Our approach is based on transposition solutions for coupled systems and both the Hilbert Uniqueness Method (HUM) and the energy multiplier method.</p>

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Boundary Controllability of a System of Petrovsky Equations Coupled by Velocities

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Mohamed Azzaoui,
  • Jawad Salhi,
  • Mouhcine Tilioua

摘要

This paper deals with the Neumann boundary controllability of a system of Petrovsky-Petrovsky type which is coupled through the velocities. We are interested in controlling the corresponding state which has two components by exerting only one boundary control force on the system. We prove that, under the usual multiplier geometric control condition and for small coupling coefficient b, there exists a time \(T_b>0\) T b > 0 such that the system is null controllable at any time \(T> T_b\) T > T b . Our approach is based on transposition solutions for coupled systems and both the Hilbert Uniqueness Method (HUM) and the energy multiplier method.