Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amadori, D., Gosse, L., Guerra, G.: Godunov-type approximation for a general resonant balance law with large data. J. Differential Equations 198, no 2, 233–274 (2004)
Audusse, E., Bouchut, F., Bristeau, M.-O., Klein, R., Perthame, B.: A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp., 25, 2050–2065 (2004)
Bachmann, F.: Analysis of a scalar conservation law with a flux function with discontinuous coefficients. Advances in Differential Equations, no 11 − 12, 1317–1338 (2004)
Bachmann, F.: PhD thesis, univ. Marseille (2005) and submitted paper
Bachmann, F.: Finite volume schemes for a nonlinear hyperbolic conservation law with a flux function involving discontinuous coefficients. Int. J. on Finite Volume (electronic), 3, no 1 (2006)
Bachmann, F., Vovelle, J.: Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Comunications in PDE, 31, 371–395 (2006)
Bouchut, F., James, F.: One-dimensional transport equations with discontinuous coefficients. Nonlinear Analysis, TMA, 32, 891–933 (1998)
Chinnayya, A., LeRoux, A.Y., Seguin N.: A well-balanced numerical scheme for shallow-water equations with topography: resonance phenomenon. Int. J. on Finite Volume (electronic), 1, no 1 (2004)
DiPerna, R.J.: Measure-valued solutions to conservation laws. Arch. Rational Mech. Anal., 88, no 3, 223–270 (1985)
Eymard, R., Gallouët, T., Herbin, R.: Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation. Chin. Ann. of Math., 16B: 1, 1–14 (1995)
Eymard, R., Gallouët, T., Herbin, R.: Finite Volume Methods. In: Ciarlet, P.G., Lions, J.L. (ed) Handbook of Numerical Analysis, Vol. VII, 713–1020, North-Holland (2000)
Gallouët, T., Hérard, J.M., Seguin, N.: Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. Fluids, 32, no 4, 479–513 (2003)
Goatin, P., LeFloch, P.G.: The Riemann problem for a class of resonant nonlinear systems of balance laws. Ann. Inst. H. Poincaré - Analyse Non-linéaire 21, 881–902 (2004)
Godlewski, E., Seguin, N.: The Riemann problem for a simple model of phase transition. Commun. Math. Sci., 4, no 1, 227–247 (2006)
Karlsen, K.H., Risebro, N.H., Towers, J.D.: L 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Sbr. K. Nor. Vid. Sel., no 3, 1–49 (2003)
Kurganov, A., Levy, D.: Central-Upwind Schemes for the Saint-Venant System. Math. Mod. and Num. An., 36, 397–425 (2002)
Perthame, B.: Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure. J. Math. Pures Appl., 77, no 10, 1055–1064 (1998)
Seguin, N., Vovelle, J.: Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. Math. Models Methods Appl. Sci., 13, no 2, 221–257 (2003)
Towers, J.D.: Convergence of a difference scheme for conservation laws with a discontinuous flux. SIAM J. Numer. Anal., 38, no 2, 681–698 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gallouët, T. (2008). Resonance and Nonlinearities. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-75712-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75711-5
Online ISBN: 978-3-540-75712-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)