Exact analysis of a nonlinear partial differential equation of gas dynamics

Sachdev, P. L. ; Dowerah, S. ; Vaganan, B. M. ; Philip, V. (1997) Exact analysis of a nonlinear partial differential equation of gas dynamics Quarterly of Applied Mathematics, 55 (2). pp. 201-229. ISSN 0033-569X

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Abstract

A new second-order nonlinear partial differntial equation is derived from one-dimensional unsteady non-isentropic gas-dynamic equations through the introduction of three "potential" functions. Appropriate boundary conditions at the shock and at the piston in terms of the new functions are obtained. The nonlinear partial differential equation is analysed in great detail. Intermediate integrals and generalized Ramann invariants are discovered. Using the classical lie group method, the direct simlarity method due to Clarkson and Kruska(1989), and equation-splitting etc., large families of new solutions are found. The direct similarity method is found to yield the most general results. Solutions with shocks ( both finite and strong) are constructed to illustrate the applicability of the solutions.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:33893
Deposited On:30 Mar 2011 13:36
Last Modified:30 Mar 2011 13:36

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