<p>We consider the mathematical model for a plate in a bounded reference configuration <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10271_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Omega \subset \mathbb {R}^n\)</EquationSource> </InlineEquation>, first with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10271_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=2\)</EquationSource> </InlineEquation>, which is interacting with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10271_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=2\)</EquationSource> </InlineEquation> magnetic fields. The latter have a damping effect. It will be shown that the arising system generates an analytic semigroup and that the estimated exponential decay rate tends to zero if the <i>n</i> constant directing magnetic vectors tend to become linearly dependent. Then, an analogous model for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10271_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=3\)</EquationSource> </InlineEquation> will be considered. In the case that there are less than <i>n</i> magnetic fields we prove the strong stability exemplarily for cubes.</p>

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Regularity and Stabilization of Magneto-Elastic Systems

  • Jaime E. Muñoz Rivera,
  • Reinhard Racke

摘要

We consider the mathematical model for a plate in a bounded reference configuration \(\Omega \subset \mathbb {R}^n\) , first with \(n=2\) , which is interacting with \(n=2\) magnetic fields. The latter have a damping effect. It will be shown that the arising system generates an analytic semigroup and that the estimated exponential decay rate tends to zero if the n constant directing magnetic vectors tend to become linearly dependent. Then, an analogous model for \(n=3\) will be considered. In the case that there are less than n magnetic fields we prove the strong stability exemplarily for cubes.