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A one dimensional analogue of the vorticity equation

Published online by Cambridge University Press:  17 April 2009

K. Sriskandarajah
K. Sriskandarajah
Affiliation:
Department of MathematicsMonash UniversityClayton Vic 3168Australia e-mail: sris@wave.maths.monash.edu.au
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Abstract

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We study the qualitative properties of the one dimensional analogue of the Helmholtz vorticity advection equation. The second order hyperbolic equation has the unusual characteristic of disturbances propagating at infinite speed. The global solution for Goursat data is given in closed form. We also obtain qualitative results on the nodal curve where the solution is zero. A related perturbation problem is considered and solutions for small data are obtained. The forced vorticity equation admits a class of soliton solutions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 119 - 134
Copyright
Copyright © Australian Mathematical Society 1997

References

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