Topology of elementary waves for mixed-type systems of conservation laws
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We construct explicitly the fundamental wave manifold for systems of two conservation laws with quadratic flux functions. We describe the shock foliation for this manifold, as well as the singular set of the foliation. We subdivide the manifold into regions where the shock curves form trivial foliations. Sonic surfaces are identified as well. We establish the stability of shock curves underC 3 perturbations of the flux functions in the Whitney topology.
- Isaacson, E L., Marchesin, D., Palmeira, C. F. B., and Plohr, B. (1992a). A global formalism for nonlinear waves in conservation laws.Commun. Math. Phys. 146, 505–552.
- Isaacson, E. L., Marchesin, D., Plohr, B., and Temple, J. B. (1992b). Multiphase flow models with singular Riemann problems.Mat. Appl. Comput. 2, 147–166.
- Lax, P. (1957). Hyperbolic systems of conservation laws II.Commun. Pure Appl. Math. 10, 537–566.
- Palmeira, C. F. B. (1977). Estabilidade diferenciável de submersŌes deR n em R. Proceedings of the 11th Brazilian Colloquium of Mathematics, PoÇos de Caldas, IMPA, pp. 789–791.
- Palmeira, C. F. B. (1978). Open manifolds foliated by planes.Ann. Math. 107, 109–131.
- Palmeira, C. F. B. (1988). Line fields defined by eigenspaces of derivatives of maps from the plane to itself. Proceedings VIth Int. Coll. Geom., Santiago de Compostella, Spain, Sept., pp. 177–205.
- Poston, T., and Stewart, I. (1978).Catastrophe Theory and Its Applications, Pitman, London, 1978.
- Steenrod, N. (1951).Topology of Fiber Bundles, Princeton University Press, Princeton, N.J.
- Smoller, J. (1983).Shock Waves and Reaction Diffusion Equations, Springer Verlag, New York.
- Schaeffer and Shearer (1987). The classification of 2×2 systems of non strictly hyperbolic conservation laws with applications to oil recovery.Commun. Pure Appl. Math. XL, 141–178.
- Topology of elementary waves for mixed-type systems of conservation laws
Journal of Dynamics and Differential Equations
Volume 6, Issue 3 , pp 427-446
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Elementary waves
- Whitney topology
- conservation laws
- shock foliation
- fundamental wave manifold