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A mathematical analysis of tsunami generation in shallow water due to seabed deformation

Published online by Cambridge University Press:  03 June 2011

Tatsuo Iguchi
Tatsuo Iguchi
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan (iguchi@math.keio.ac.jp)
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Abstract

In numerical computations of tsunamis due to submarine earthquakes, it is frequently assumed that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero and the shallow-water equations are often used to simulate the propagation of tsunamis. We give a mathematically rigorous justification of this tsunami model starting from the full water-wave problem by comparing the solution of the full problem with that of the tsunami model. We also show that, in some cases, we have to impose a non-zero initial velocity field, which arises as a nonlinear effect.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 3 , June 2011 , pp. 551 - 608
Copyright
Copyright © Royal Society of Edinburgh 2011

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