Title: | A new numerical model for propagation of tsunami waves (English) |

Author: | Švadlenka, Karel |

Language: | English |

Journal: | Kybernetika |

ISSN: | 0023-5954 |

Volume: | 43 |

Issue: | 6 |

Year: | 2007 |

Pages: | 893-902 |

Summary lang: | English |

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Category: | math |

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Summary: | A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model. (English) |

Keyword: | long waves |

Keyword: | nonlinear hyperbolic equation |

Keyword: | volume constraint |

Keyword: | free boundary |

Keyword: | variational method |

Keyword: | discrete Morse semi-flow |

Keyword: | FEM |

MSC: | 35L70 |

MSC: | 35R35 |

MSC: | 47J30 |

MSC: | 58E50 |

MSC: | 74J15 |

MSC: | 76B15 |

MSC: | 86A05 |

idZBL: | Zbl 1140.35529 |

idMR: | MR2388402 |

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Date available: | 2009-09-24T20:30:56Z |

Last updated: | 2013-09-21 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135824 |

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Reference: | [1] Bona J. L., Chen M., Saut J.-C.: Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media.I: Derivation and linear theory. J. Nonlinear Sci. 12 (2002), 283–318 Zbl 1059.35103, MR 1915939, 10.1007/s00332-002-0466-4 |

Reference: | [2] Kikuchi N.: An approach to the construction of Morse flows for variational functionals.In: Nematics – Mathematical and Physical Aspects (J. M. Coron, J. M. Ghidaglia, and F. Hélein, eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332 (1991), Kluwer Academic Publishers, Dodrecht – Boston – London, pp. 195–198 Zbl 0850.76043, MR 1178095 |

Reference: | [3] Nagasawa T., Omata S.: Discrete Morse semiflows of a functional with free boundary.Adv. Math. Sci. Appl. 2 (1993), 147–187 Zbl 0795.35150, MR 1239254 |

Reference: | [4] Omata S.: A numerical method based on the discrete Morse semiflow related to parabolic and hyperbolic equations.Nonlinear Anal. 30 (1997), 2181–2187 MR 1490340, 10.1016/S0362-546X(97)00397-0 |

Reference: | [5] Švadlenka K., Omata S.: Construction of weak solution to hyperbolic problem with volume constraint.Submitted to Nonlinear Anal |

Reference: | [6] Yamazaki T., Omata S., Švadlenka, K., Ohara K.: Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation.Adv. Math. Sci. Appl. 16 (2006), 57–67 Zbl 1122.35159, MR 2253225 |

Reference: | [7] Yoshiuchi H., Omata S., Švadlenka, K., Ohara K.: Numerical solution of film vibration with obstacle.Adv. Math. Sci. Appl. 16 (2006), 33–43 Zbl 1122.35160, MR 2253223 |

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