Exact solutions for some non-conservative hyperbolic systems
| Autor: | K. T. Joseph, P. L. Sachdev |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Pure mathematics
Partial differential equation Non conservative Generalization Applied Mathematics Mechanical Engineering Mathematical analysis Hyperbolic systems symbols.namesake Exact solutions in general relativity Riemann problem Mechanics of Materials symbols Initial value problem Hyperbolic partial differential equation Mathematics |
| Zdroj: | International Journal of Non-Linear Mechanics. 38:1377-1386 |
| ISSN: | 0020-7462 |
| DOI: | 10.1016/s0020-7462(02)00077-x |
| Popis: | 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). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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