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The Quarterly Journal of Mechanics and Applied Mathematics 1964 17(3):351-367; doi:10.1093/qjmam/17.3.351
© 1964 by Oxford University Press
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THE ASYMPTOTIC DISPERSION RELATIONSHIP FOR A GENERAL LINEARIZED SYSTEM OF DIFFERENTIAL EQUATIONS OF FLUID-DYNAMICAL TYPE

R. HERDAN {dagger}

( Research Laboratory, Associated Electrical Industries, Aldermaston Court Aldermaston, Berkshire, England )

In this paper we consider the local dispersion relation for a system of n linear, first order equations of the form


with real, finite characteristic speeds in any direction. The coefficients may be functions of position. It is shown how to obtain explicitly for each branch of the dispersion relation the appropriate asymptotic expansion for the complex angular frequency {omega} in terms of the real wave number {kappa}. It is found that each of these is connected with one or other of the characteristic speeds. Both the hyperbolic and non-hyperbolic cases are considered.


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