A note on uniqueness and compact support of solutions in a recent model for tsunami background flows

Anna Geyer

doi:10.3934/cpaa.2012.11.1431

Article Contents

2012, Volume 11, Issue 4: 1431-1438. Doi: 10.3934/cpaa.2012.11.1431

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A note on uniqueness and compact support of solutions in a recent model for tsunami background flows

Anna Geyer^1,

1.
Nordbergstrasse 15, UZA 2, 2A 287, 1090 Wien

Received: April 30, 2011

Revised: August 31, 2011

Published: June 2012

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Abstract

We present an elementary proof of uniqueness for solutions of an initial value problem which is not Lipschitz continuous, generalizing a technique employed in [20]. This approach can be applied for a wide class of vorticity functions in the context of [6], where, departing from a recent model for the evolution of tsunami waves developed in [10], the possibility of modelling background ows with isolated regions of vorticity is rigorously established.

Keywords:

Nonlinear water waves with vorticity,
tsunami background flow,
uniqueness and compact support of solutions.

Mathematics Subject Classification: Primary: 34A34, 34A12; Secondary: 35Q31, 35J61.

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References

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