Prasad, Phoolan (2016) Ray equations of a weak shock in a hyperbolic system of conservation laws in multi-dimensions. In: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 126 (2). pp. 199-206.
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Abstract
In this paper we give a complete proof of a theorem, which states that `for a weak shock, the shock ray velocity is equal to the mean of the ray velocities of nonlinear wavefronts just ahead and just behind the shock, provided we take the wavefronts ahead and behind to be instantaneously coincident with the shock front. Similarly, the rate of turning of the shock front is also equal to the mean of the rates of turning of such wavefronts just ahead and just behind the shock'. A particular case of this theorem for shock propagation in gasdynamics has been used extensively in applications. Since it is useful also in other physical systems, we present here the theorem in its most general form.
| Item Type: | Journal Article |
|---|---|
| Publication: | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES |
| Publisher: | INDIAN ACAD SCIENCES |
| Additional Information: | Copy right for this article belongs to the INDIAN ACAD SCIENCES, C V RAMAN AVENUE, SADASHIVANAGAR, P B #8005, BANGALORE 560 080, INDIA |
| Keywords: | Ray theory; nonlinear waves; conservation laws; shock propagation and weak curved shock |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 17 Jun 2016 05:07 |
| Last Modified: | 17 Jun 2016 05:07 |
| URI: | http://eprints.iisc.ac.in/id/eprint/53969 |
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