Asymptotic time-behavior for weighted scalar conservation laws
Le Floch, Philippe ; Nedelec, J. C.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988), p. 469-475 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1988-01-01
@article{M2AN_1988__22_3_469_0,
     author = {Le Floch, Philippe and Nedelec, J. C.},
     title = {Asymptotic time-behavior for weighted scalar conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {22},
     year = {1988},
     pages = {469-475},
     mrnumber = {958879},
     zbl = {0683.35051},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1988__22_3_469_0}
}

Le Floch, Philippe; Nedelec, J. C. Asymptotic time-behavior for weighted scalar conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988) pp. 469-475. http://gdmltest.u-ga.fr/item/M2AN_1988__22_3_469_0/

[1] E. D. Conway, The formation and decay of shocks for a conservation law in several dimensions, Arch. Rat. M.A. 64 (1977) pp. 47-57. | MR 427850 | Zbl 0352.35029

[2] C. M . Dafermos, Characteristics in hyperbolic conservation law, in « Nonlinear analysis and mechanics : Heriot-Watt Symposium vol. 1 », Knops Editor (1983). | Zbl 0373.35048

[3]. F. Dubois, Ph. Le Floch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Internal Report (1987), École Polytechnique ; J. of Diff. Eq., Vol. 71, No 1, jan. 1988, pp. 93-122. | MR 922200 | Zbl 0649.35057

[4] F. Dubois, Ph. Le Floch, Condition à la limite pour un système de lois de conservation, Note Compt. Rend. Acad. Sc. Paris, t. 304, Série I, n° 3, pp. 75-78 (1987). | MR 878830 | Zbl 0634.35046

[5] B. Keyfitz, Solutions with shocks, an example of Ll -contractive semi-group, Comm. Pure Appl. Math., 24 (1971) pp. 125-132. | MR 271545 | Zbl 0206.10401

[6] S. N. Kruskov, First order quasi-linear equations in several independant variables, Math. USSR Sb., 10 1970) n° 2, pp. 217-243.

[7] P. D. Lax, Conservation laws and the mathematical theory of shock waves, CBMS Ser. Appl. Math, vol. 11, SIAM, Philadelphia (1973). | MR 350216 | Zbl 0268.35062

[8] Ph. Le Floch, Explicit formula for scalar conservation laws with boundary conditions, to appear in Math. Meth. in Appl. Sc. (1988) vol. 10. | MR 949657 | Zbl 0679.35065

[9] Ph. Le Floch, Generalized Riemann problem and boundary conditions for systems of conservation laws, Thesis (1987) École Polytechnique (France).

[10] Ph. Le Floch, J. C. Nedelec, Explicit formula for weighted scalar conservation laws, Internal Report n° 144 (janv. 1986) of École Polytechnique ; accepted for publication to Transactions of A.M.S.

[11] Ph. Le Floch, J. C. Nedelec, Lois de conservation scalaires avec poids, Note Compt. Rend. Acad. Sc. Paris, t. 301, Série I, n° 17, pp. 1301-1304 (1985). | MR 822833 | Zbl 0612.35084

[12] Ph. Le Floch, P. A. Raviart, Un développement asymptotique pour le problème de Riemann généralisé, Compt. Rend. Acad. Se. Paris, t. 304, Série I, n° 4, pp. 119-122 (1987) and Ann. Henri Poincaré, Analyse non linéaire. | MR 890629 | Zbl 0619.35074

[13] T. P. Liu, M. Pierre, Source-solutions and asymptotic behavior in conservation laws, J. of Diff. Eq. 51, 419-441 (1984). | MR 735207 | Zbl 0545.35057

[14] O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, A.M.S. Transal., Ser. 2, 26, pp. 95-172 (1963).

[15] M.E. Schonbek, Existence of solutions to singular conservation laws, Siam J. Math. Anal., vol. 15, n° 6 (nov. 1984). | MR 762969 | Zbl 0567.35060

[16] J. A. Smoller, Reaction-Diffusion Equations and Shock Waves, Springer, Verlag 258 (1983).

[17] G.B. Whitham, Linear and Non linear Waves, Wiley Interscience, New York (1974). | MR 483954 | Zbl 0373.76001