Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

Prasad, Phoolan (1975) Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic. In: Journal of Mathematical Analysis and Applications, 50 (3). pp. 470-482.

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Abstract

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Item Type:	Journal Article
Publication:	Journal of Mathematical Analysis and Applications
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	23 Oct 2009 04:34
Last Modified:	19 Sep 2010 05:48
URI:	http://eprints.iisc.ac.in/id/eprint/24108

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