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# Evolution equations on non flat waveguides

Type of Publication: | Working Paper/Technical Report |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-123838 |

Author: | D'Ancona, Piero; Racke, Reinhard |

Year of publication: | 2010 |

Series: | Konstanzer Schriften in Mathematik ; 273 |

Summary: |
We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator
H=-Delta_{x}-Delta_{y}+V(x,y) with Dirichled boundary condition on an unbounded domain Omega, and we introduce the notion of a repulsive waveguide along the direction of the first group of variables x. If Omega is a repulsive waveguide, we prove a sharp estimate for the Helmholtz equation Hu-lambda u=f. As consequences we prove smoothing estimates for the Schrödinger and wave equations associated to H, and Strichartz estimates for the Schrödinger equation. Additionally, we deduce that the operator H does not admit eigenvalues. |

Subject (DDC): | 510 Mathematics |

Controlled Keywords (GND): | Schrödinger-Gleichung |

Link to License: | Terms of use |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:2b93fb686f1c8e47e1de3e14b69d08d8

D'ANCONA, Piero, Reinhard RACKE, 2010. Evolution equations on non flat waveguides

@techreport{DAncona2010Evolu-630, series={Konstanzer Schriften in Mathematik}, title={Evolution equations on non flat waveguides}, year={2010}, number={273}, author={D'Ancona, Piero and Racke, Reinhard} }

dara2010.pdf | 99 |