A structurally damped plate equation with Dirichlet-Neumann boundary conditions

Denk, Robert; Schnaubelt, Roland

A structurally damped plate equation with Dirichlet-Neumann boundary conditions

Files

Denk_0-253353.pdf(587.15 KB)

Date

2014

Authors

Denk, Robert

Schnaubelt, Roland

Series

Konstanzer Schriften in Mathematik; 330

Publication type

Working Paper/Technical Report

Abstract

We investigate sectoriality and maximal regularity in L^p-L^q-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.

Subject (DDC)

510 Mathematics

Keywords

Structurally damped plate equation, clamped boundary condition, R-sectoriality

Cite This

ISO 690

DENK, 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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