A structurally damped plate equation with Dirichlet-Neumann boundary conditions

Kurzanzeige
dc.contributor.authorDenk, Robert
dc.contributor.authorSchnaubelt, Roland
dc.date.accessioned2015-09-16T13:34:39Z
dc.date.available2015-09-16T13:34:39Z
dc.date.issued2015eng
dc.description.abstractWe 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.eng
dc.description.versionpublished
dc.identifier.doi10.1016/j.jde.2015.02.043eng
dc.identifier.urihttp://kops.uni-konstanz.de/handle/123456789/31760
dc.language.isoengeng
dc.subjectStructurally damped plate equation, Clamped boundary condition, R-sectoriality, Optimal regularity, Operator-valued Fourier multipliers, Exponential stabilityeng
dc.subject.ddc510eng
dc.titleA structurally damped plate equation with Dirichlet-Neumann boundary conditionseng
dc.typeJOURNAL_ARTICLEeng
dspace.entity.typePublication
kops.citation.bibtex
@article{Denk2015struc-31760,
  year={2015},
  doi={10.1016/j.jde.2015.02.043},
  title={A structurally damped plate equation with Dirichlet-Neumann boundary conditions},
  number={4},
  volume={259},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={1323--1353},
  author={Denk, Robert and Schnaubelt, Roland}
}
kops.citation.iso690DENK, Robert, Roland SCHNAUBELT, 2015. A structurally damped plate equation with Dirichlet-Neumann boundary conditions. In: Journal of Differential Equations. 2015, 259(4), pp. 1323-1353. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.043deu
kops.citation.iso690DENK, Robert, Roland SCHNAUBELT, 2015. A structurally damped plate equation with Dirichlet-Neumann boundary conditions. In: Journal of Differential Equations. 2015, 259(4), pp. 1323-1353. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.043eng
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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;. 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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kops.sourcefieldJournal of Differential Equations. 2015, <b>259</b>(4), pp. 1323-1353. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.043deu
kops.sourcefield.plainJournal of Differential Equations. 2015, 259(4), pp. 1323-1353. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.043deu
kops.sourcefield.plainJournal of Differential Equations. 2015, 259(4), pp. 1323-1353. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.043eng
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source.bibliographicInfo.fromPage1323eng
source.bibliographicInfo.issue4eng
source.bibliographicInfo.toPage1353eng
source.bibliographicInfo.volume259eng
source.identifier.eissn1090-2732eng
source.identifier.issn0022-0396eng
source.periodicalTitleJournal of Differential Equationseng
temp.internal.duplicates<p>Möglicherweise Dublette von: </p><a href="http://kops.uni-konstanz.de/handle/123456789/29060">http://kops.uni-konstanz.de/handle/123456789/29060</a><p>Letzte Überprüfung: 23.06.2015 14:53:25</p>deu

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