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

Type of Publication: | Working Paper/Technical Report |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-253353 |

Author: | Denk, Robert; Schnaubelt, Roland |

Year of publication: | 2014 |

Series: | Konstanzer Schriften in Mathematik ; 330 |

Summary: |
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 C^{4}.It turns out that the first-order system related to the scalar equation on R ^{n} 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 |

Link to License: | In Copyright |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:7190374e4fa5cebcf4117faa5f47c72f

DENK, Robert, Roland SCHNAUBELT, 2014. A structurally damped plate equation with Dirichlet-Neumann boundary conditions

@techreport{Denk2014struc-29060, series={Konstanzer Schriften in Mathematik}, title={A structurally damped plate equation with Dirichlet-Neumann boundary conditions}, year={2014}, number={330}, author={Denk, Robert and Schnaubelt, Roland} }

Denk_0-253353.pdf | 382 |