| 概要 |
In numerical simulation of tsunamis due to submarine earthquakes, one usually uses the shallow water equations by assuming that the initial displacement of water surface is equal to the permanent deformation of seabed and that there is no initial velocity field. In this talk, starting from the full water wave problem (a free boundary problem for an irrotational flow of an incompressible ideal fluid under the gravitational field) we derive mathematically rigorously the shallow water model mentioned above, that is, we will show that the solution of the full water wave problem can be approximated by the solution of the shallow water model in some limits of parameters. Moreover, we report that in some case we have to take some initial velocity field, which arises as a nonlinear effect, into account as initial data.
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