## A structurally damped plate equation with Dirichlet-Neumann boundary conditions

2014
##### Authors
Schnaubelt, Roland
##### Series
Konstanzer Schriften in Mathematik; 330
##### Publication type
Working Paper/Technical Report
##### Abstract
We investigate sectoriality and maximal regularity in Lp-Lq-Sobolev spaces for the structurally damped plate equation with Dirichlet-Neumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C4.

It turns out that the first-order system related to the scalar equation on Rn is sectorial only after a shift in the operator. On the half-space one has to include zero boundary conditions in the underlying function space in order to obtain sectoriality of the shifted operator and maximal regularity for the case of homogeneous boundary conditions. We further show that the semigroup solving the problem on bounded domains is exponentially stable.
510 Mathematics
##### Keywords
Structurally damped plate equation, clamped boundary condition, R-sectoriality
##### Cite This
ISO 690DENK, Robert, Roland SCHNAUBELT, 2014. A structurally damped plate equation with Dirichlet-Neumann boundary conditions
BibTex
@techreport{Denk2014struc-29060,
year={2014},
series={Konstanzer Schriften in Mathematik},
title={A structurally damped plate equation with Dirichlet-Neumann boundary conditions},
number={330},
author={Denk, Robert and Schnaubelt, Roland}
}

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<dcterms:abstract xml:lang="eng">We investigate sectoriality and maximal regularity in L&lt;sup&gt;p&lt;/sup&gt;-L&lt;sup&gt;q&lt;/sup&gt;-Sobolev spaces for the structurally damped plate equation  with Dirichlet-Neumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in  bounded  domains of class C&lt;sup&gt;4&lt;/sup&gt;.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;It turns out that the first-order system related to the scalar equation on R&lt;sup&gt;n&lt;/sup&gt; is sectorial only after a shift in the operator. On the half-space one has to include zero boundary conditions in the underlying function space in order to obtain sectoriality of the shifted operator and maximal regularity for the case of homogeneous boundary conditions. We further show that the semigroup solving the problem on bounded domains is exponentially stable.</dcterms:abstract>
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Yes