Joseph, KT and Sachdev, PL (2003) Exact solutions for some non-conservative hyperbolic systems. In: International Journal of Non-Linear Mechanics, 38 (9). pp. 1377-1386.
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In this paper, we study initial value problem for some non-conservative hyperbolic systems of partial differential equations of first order. The first one is the Riemann problem for a model in elastodynamics and the second o e the initial value problem for a system which is a generalization of the Hopf equation. The non-conservative products which appear in the equations do not make sense in the classical theory of distributions and are understood in the sense of Volpert (Math. USSR Sb. 2 (1967) 225). Following Lax (Comm. Pure Appl. Math. 10 (1957) 537) and Dal Maso et al. (J. Math. Pures Appl. 74 (1995) 483), we give an explicit solution for the Riemann problem for the elastodynamics equation. The coupled Hopf equation is studied using a generalization of the method of Hopf (Comm. Pure Appl. Math. 3 (1950) 201).
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Keywords:||Non-conservative hyperbolic systems;Initial value problems; Exact solutions.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||19 Jul 2009 04:39|
|Last Modified:||19 Sep 2010 04:54|
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