@book{MSMF_1994_2_56__1_0, author = {Sevennec, Bruno}, title = {G\'eom\'etrie des syst\`emes hyperboliques de lois de conservation}, series = {M\'emoires de la Soci\'et\'e Math\'ematique de France}, publisher = {Soci\'et\'e math\'ematique de France}, number = {56}, year = {1994}, doi = {10.24033/msmf.370}, mrnumber = {95g:35123}, zbl = {0807.35090}, language = {fr}, url = {http://archive.numdam.org/item/MSMF_1994_2_56__1_0/} }
TY - BOOK AU - Sevennec, Bruno TI - Géométrie des systèmes hyperboliques de lois de conservation T3 - Mémoires de la Société Mathématique de France PY - 1994 IS - 56 PB - Société mathématique de France UR - http://archive.numdam.org/item/MSMF_1994_2_56__1_0/ DO - 10.24033/msmf.370 LA - fr ID - MSMF_1994_2_56__1_0 ER -
Sevennec, Bruno. Géométrie des systèmes hyperboliques de lois de conservation. Mémoires de la Société Mathématique de France, Serie 2, no. 56 (1994), 132 p. doi : 10.24033/msmf.370. http://numdam.org/item/MSMF_1994_2_56__1_0/
[A1] Méthodes mathématiques de la mécanique classique, Mir 1976. | Zbl | MR
,[A2] Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Mir 1978. | Zbl
,[Ba] Apparition éventuelle de singularités dans les problèmes d'évolution non linéaires, séminaire Bourbaki No 555 (1980). | Zbl | Numdam
,[Bla] Vorlesungen über Differentialgeometrie ; II, Affine Differentialgeometrie, Berlin, J. Springer, 1923, cf. aussi Gesammelte Werke, Band IV (Burau, Chern et al editors), Thales, Essen, 1985.
,[Bo1] Chocs caractéristiques, C.R.A.S. 274, sér. A, 1018-1021 (1972). | Zbl | MR
,[Bo2] Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systèmes hyperboliques, C.R.A.S. 278, sér. A, 909-912 (1974). | Zbl | MR
,[Bo3] Symétrisation des systèmes d'équations aux dérivées partielles avec densité d'énergie convexe et contraintes, C.R.A.S. 295, sér. 1, 551-554 (1982). | Zbl | MR
,[B-H] Rotationnaly invariant hyperbolic waves, C.P.A.M. 43 (1990), 1037-1053. | Zbl | MR
, ,[Chk] Normal connection in the geometry of normalized submanifolds of affine space, Soviet Math. (Plenum Publ. Corp.), 2131-2140 (1991). | Zbl
,[Co-D] Zbl
, , Z. Angew. Math. Phys. 22, 691-702 (1971). |[Co-S1] Shock waves as limits of progressive wave solutions of higher order equations, C.P.A.M. 24, 459-472 (1971), Part II : C.P.A.M. 25, 133-146 (1972). | Zbl | MR
, ,[Co-S2] On the structure of magnetohydrodynamic shock waves, C.P.A.M. 27, 367-375 (1974). | Zbl | MR
, ,[Daf1] The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Diff. Eqs 20, 90-114 (1976). | Zbl | MR
,[Daf2] Hyperbolic systems of conservation laws, “Systems of nonlinear partial differential equations”, J. Ball (ed.), NATO ASI series C, No. 111, Reidel Publ. Co., 25-70 (1983). | Zbl | MR
,[Daf3] Quasilinear hyperbolic systems with involutions, Arch. Rat. Mech. Anal., 94, 373-389 (1986). | Zbl | MR
,[Daf4] Admissible wave fans in nonlinear hyperbolic systems, Arch. Rat. Mech. Anal., 106:3, 243-260 (1989). | Zbl | MR
,[Daf5] Generalized characteristics in hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal., 107:2, 127-157 (1989). | Zbl | MR
,[Dar1] Leçons sur la théorie générale des surfaces. Partie IV, Gauthier-Villars 1946. | Zbl
,[Dar2] Leçons sur les systèmes orthogonaux et les coordonnées curvilignes, Gauthier-Villars 1910. | JFM
,[Di-V] Affine differential geometry of hypersurfaces, Geometry and Topology of Submanifolds II, Avignon 1988 (World Scientific 1990), 144-164. | Zbl | MR
, ,[DiP1] Global solutions to a class of nonlinear hyperbolic systems of equations, C.P.A.M. 26, 1-28 (1973). | Zbl | MR
,[DiP2] Existence in the large for quasilinear hyperbolic conservation laws, Arch. Rat. Mech. Anal. 52, 244-257 (1973). | Zbl | MR
,[DiP3] Decay of solutions of hyperbolic systems of conservation laws with a convex extension, Arch. Rat. Mech. Anal. 64, 1-46 (1977). | Zbl | MR
,[DiP4] Uniqueness of solutions of nonlinear hyperbolic systems of conservation laws, Indiana Univ. Math. J. 28, 137-188 (1979). | Zbl | MR
,[DiP5] Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82, 27-70 (1983). | Zbl | MR
,[DiP6] Measure-valued solutions to conservation laws, Arch. Rat. Mech. Anal. 88, 223-270 (1985). | Zbl | MR
,[DiP-M] The validity of geometrical optics for weak solutions of conservation laws, Comm. Math. Phys. 98, 313-347 (1985). | Zbl | MR
, ,[Du-N1] Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Russian Math. Surveys 44:6, 35-124 (1989). | Zbl | MR
, ,[Du-N2] Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method, Soviet Math. Dokl. Vol 27, no3, 665-669 (1983). | Zbl | MR
, ,[Dy] Cauchy's problem for quasilinear sytems, Sov. Math. Dokl. 2, 7-8 (1961). | Zbl
,[Fe1] Hamiltonian systems of hydrodynamic type and their realization on hypersurfaces of a pseudo-euclidean space, Journal of Sov. Math., p. 1970-1995, Plenum (1991). | Zbl | MR
,[Fe2] Integration of weakly nonlinear hydrodynamic systems in Riemann invariants, Physics Letters A, p. 112-118, (1991). | MR
,[Fe-P] Quasiclassical limit of coupled KdV equations. Riemann invariants and multihamiltonian structure. Physica D, 52, (1991) 211-219. | Zbl | MR
, ,[Fi-G] Mathematical aspects of electrophoresis, Proc. Heriot-Watt 1988 : Reaction-Diffusion Equations, Oxford Univ. Press.
, ,[Fre1] Anomale Schocks, strukturell labile Lösungen und die Geometrie der Rankine-Hugoniot Bedingungen, Thèse, Ruhr-Universität Bochum (1987).
,[Fre2] On compact linear degeneracy, IMA preprint 551, University of Minnesota, (1989).
,[Fre3] Rotationnal degeneracy of hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal. 113, 1991, 39-64. | Zbl
,[Fri] On the laws of relativistic electro-magneto-fluid dynamics, C.P.A.M. 27, 749-808 (1974). | Zbl | MR
,[Fri-L] Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA 68, 1686-1688 (1971). | Zbl | MR
, ,[F-R-S] On the crossing rule, C.P.A.M. 37, 19-37 (1984). | Zbl | MR
, , ,[Ga] Korteweg-de Vries equation and generalizations. IV : the Korteweg-de Vries equation as a Hamiltonian system, J. Math. Phys 12 (1971), 1548-1551. | Zbl | MR
,[Gel] Some problems in the theory of quasilinear equations, A.M.S. Trans. Ser. 2, No 29, 295-381 (1963). | Zbl | MR
,[Ger] Contribution à la théorie des ondes de choc en magnétodynamique des fluides, ONERA Publ. No 97, Paris 1959. | MR
,[Gl] Solutions in the large for nonlinear hyperbolic systems of equations, C.P.A.M. 18, 697-715 (1965). | Zbl | MR
,[Gl-L] Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. A.M.S. No 101, Providence 1970. | Zbl | MR
, ,[Go1] On the concept of generalized solution, Sov. Math. Dokl. 1, 1194-1196 (1960). | Zbl | MR
,[Go2] On non-unique "blurring" of discontinuities in solutions of quasilinear systems, Sov. Math. Dokl. 2, 43-44 (1961). | Zbl | MR
,[Go3] An interesting class of quasilinear systems, Sov. Math. Dokl. 2, 947-949 (1961). | Zbl
,[Go4] Lois de conservation et intégrales d'énergie des équations hyperboliques, Proc. 1986 Nonlinear Hyperbolic Problems XV, p. 135-149, C. Carasso, P.A. Raviart, D. Serre eds., Lect. Notes Math. 1270, Springer-Verlag 1987. | Zbl
,[Gue] Problèmes mixtes hyperboliques quasilinéaires caractéristiques, Thèse, Université de Rennes-1, (1989).
,[Gui-St] Symplectic techniques in physics, Cambridge Univ. Press, 1984. | Zbl | MR
, ,[Ha-L-vL] On upstream differencing and Godunov-type schemes for hyperbolic systems of conservation laws, SIAM Review, 25, 1, 35- (1983). | Zbl | MR
, , ,[Hb1] Etude variationnelle du problème de Riemann, Thèse, Lyon 1989.
,[Hb2] Régularité des solutions du problème de Riemann, Comm. in P.D.E., 15, 5, 693-709 (1990). | Zbl | MR
,[Hb3] Existence et unicité des solutions pour certains systèmes de lois de conservation, Prepubl. ENS-Lyon no 32, (1990) (à paraître dans Arch. Rat. Mech. Anal.). | MR
,[Hb4] Error estimates for oscillating solutions to hyperbolic systems of conservation laws, Comm. in P.D.E., 18, 2, 281-304 (1993). | Zbl | MR
,[Hel] Differential geometry, Lie groups, and symmetric spaces, Acad. Press, New York, 1978. | Zbl
,[H-M-R] Resonantly interacting weakly nonlinear waves. II. Several space variables, Stud. Appl. Math. 75, 187-226 (1986). | Zbl | MR
, , ,[Je] Quasilinear hyperbolic systems and waves, Pitman, London 1976. | Zbl | MR
,[Jn] Formation of singularities in one-dimensional nonlinear wave propagation, C.P.A.M., Vol 27, 377-405 (1974). | Zbl | MR
,[Jo-M-R1] Rigorous resonant 1-d nonlinear geometric optics, Journées EDP, St-Jean de Monts, 1990. | Numdam | Zbl | MR | EuDML
, , ,[Jo-M-R2] Formal and rigorous nonlinear high frequency waves, Proc. Nonlin. Hyp. Eq., Como 1990, Pitman. (à paraître)
, , ,[Jou] Sur la propagation des discontinuités dans les fluides, C.R.A.S. 132, 673-676 (1901). | JFM
,[K-K1] The Riemann problem for some nonstrictly hyperbolic systems of conservation laws, Notices AMS, 23 (1976), A-127-128.
, ,[K-K2] Existence and uniqueness of entropy solutions to the Riemann problem for hyperbolic systems of two non-linear conservation laws, J. Diff. Equ., 27 (1978), 444-476. | Zbl | MR
, ,[K-K3] A system of non-stictly hyperbolic conservation laws arising in elasticity theory, Arch. Rat. Mech. Anal., 72 (1980) 219-241. | Zbl | MR
, ,[K-N] Foundations of differential geometry I,II, Wiley Interscience, New York, 1963,1969. | Zbl
, ,[Kru] First order quasilinear equations in several independent variables, Math. USSR Sb. 10, 217-242 (1970). | Zbl
,[K-T] A certain generalization of a theorem of Glimm, Dokl. Akad. Nauk. SSSR, 221, 287-290 (1975). | Zbl | MR
, ,[Law] The quantitative theory of foliations, CBMS-NSF Reg. Conf. Ser. in Math. No 27, AMS, Providence, 1977. | Zbl | MR
,[Lax1] The initial value problem for nonlinear hyperbolic equation in two independent variables, Ann. of Math. Studies 33, Princeton, 211-229 (1954). | Zbl | MR
,[Lax2] Hyperbolic systems of conservation laws: II, CPAM Vol 10, 537-566 (1957). | Zbl | MR
,[Lax3] Shock waves and entropy, Contributions to nonlinear functional analysis, Zarantonello ed., p. 603-634, NY Academic Press, 1971. | Zbl | MR
,[Lax4] The formation and decay of shock waves, Amer. Math. Monthly 79, 227-241 (1972). | Zbl | MR
,[Lax5] Hyperbolic systems of conservation laws and the mathematical theory of shock waves, CBMS-NSF Reg. Conf. Ser. in Appl. Math. no 11 SIAM (1973). | Zbl | MR
,[Lax6] The multiplicity of eigenvalues, B.A.M.S. Vol 6 No 2, 213-214 (1982). | Zbl | MR
,[Lax-Lv] The small dispersion limit for the KdV equation I, II & III, C.P.A.M. 36 (1983), 253-290, 571-593, 809-830 | Zbl | MR
, ,[Lev] The hyperbolic nature of the zero dispersion KdV limit, Comm. Part. Diff. Equ., 13 (1988), 495-514. | Zbl | MR
,[Li1] Existence and uniqueness for Riemann problems, Trans. A.M.S., 212, 375-382 (1975). | Zbl | MR
,[Li2] The Riemann problem for general systems of conservation laws, J. Diff. Eqs., 18, 218-234 (1975). | Zbl | MR
,[Li3] Solutions in the large for the equations of nonisentropic gas dynamics, Indiana Univ. Math. J. 26,1, 147-177 (1977). | Zbl | MR
,[Li4] The deterministic version of the Glimm scheme, Comm. Math. Phys. 57, 135-148 (1977). | Zbl | MR
,[Li5] Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations, J. Diff. Eqs, 33, 92-111 (1979). | Zbl | MR
,[Li6] Admissible solutions of hyperbolic conservation laws, Mem. A.M.S. No 240, Providence 1981. | Zbl | MR
,[Ma-P] Stable viscosity matrices for systems of conservation laws, J. Diff. Eqs. 56, 229-262 (1985). | Zbl | MR
, ,[Ma-R] Resonantly interacting weakly nonlinear waves. I. A single space variable, Stud. Appl. Math. 71, 149-179 (1984). | Zbl | MR
, ,[Ma-R-S] A canonical system of integro-differential equations arising in resonant nonlinear acoustics, Stud. Appl. Math. 79, 205-262 (1988). | Zbl | MR
, , ,[Mo1] Systems of conservation laws of mixed type, J. Diff. Eqs. 37, 70-88 (1980). | Zbl | MR
,[Mo2] A topological degree for orbits connecting critical points of autonomous systems, J. Diff. Eqs. 38, 176-191 (1980). | Zbl | MR
,[Mo3] Existence in the large for Riemann problems for systems of conservation laws, Trans. A.M.S. 292, 375-381 (1985). | Zbl | MR
,[Mo4] Uniqueness failure for entropy solutions of hyperbolic systems of conservation laws, C.P.A.M. 42, 173-183 (1989), erratum C.P.A.M. 43, 295-297 (1990). | Zbl | MR
,[Mo5] The rate of total entropy generation for Riemann problems, J. Diff. Eqs. 87, 115-143 (1990). | Zbl | MR
,[Mo-F] Nonlocal hamiltonian operators of hydrodynamic type and constant curvature metric, Russ. Math. Surv. 45, 3 (1990) 218-219. | Zbl | MR
, ,[Ni-Sm] Solutions in the large for some nonlinear hyperbolic conservation laws, C.P.A.M. 26, 183-200 (1973). | Zbl | MR
, ,[No-Pi] Cubic form theorem for affine immersions, Results in Math. (Birkhäuser), 13, 338-362 (1988). | Zbl | MR
, ,[Ole1] Cauchy's problem for nonlinear equations in a class of discontinuous functions, Dokl. 95 (1954), A.M.S. Transl. (2) 42, 7-12 (1964). | Zbl | MR
,[Ole2] Discontinuous solutions of nonlinear differential equations, Uspekhi (1957), A.M.S. Transl. (2) 26, 95-172 (1963). | Zbl
,[Ole3] Uniqueness and stability of the generalized solutions of the Cauchy problem for a quasilinear equation, Uspekhi (1959), A.M.S. Transl. (2) 33, 285-290 (1963). | Zbl
,[Olv] Applications of Lie groups to differential equations, Springer Verlag, 1986. | Zbl | MR
,[Ovs] Group analysis of differential equations, Acad. Press, 1982. | Zbl | MR
,[Peg] Some explicit resonating waves in weakly nonlinear gas dynamics, Stud. Appl. Math. 79, 263-270 (1988). | Zbl | MR
,[Ran] On the thermodynamical theory of waves of finite longitudinal disturbance, Phil. Trans. Roy. Soc. Lond. 160, 277-288 (1870). | JFM
,[Rie] Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Ges. Werke, Leipzig, 157-175 (1892).
,[Sch] Continuous Glimm functionals and uniqueness of solutions of the Riemann problem, Ind. Univ.Math.J. 34, 533-589 (1985). | Zbl | MR
,[Ser1] Systèmes hyperboliques non-linéaires commutant entre eux, Prepubl. Lyon-St Etienne No 26 (1984).
,[Ser2] Compacité par compensation et systèmes hyperboliques de lois de conservation, C.R.Acad.Sc. Paris, t. 299, ser.I, No 20, p.555-558 (1984). | Zbl | MR
,[Ser3] La compacité par compensation pour les systèmes hyperboliques non-linéaires de deux équations à une dimension d'espace, J.M.P.A. 65, 423-468 (1986). | Zbl | MR
,[Ser4] Solutions à variation bornée pour certains systèmes hyperboliques de lois de conservation, J. of Diff. Equ. 68, 137-169 (1987). | Zbl | MR
,[Ser5] Domaines invariants pour les systèmes hyperboliques de lois de conservation, J. of Diff. Equ. 69, 46-62 (1987). | Zbl | MR
,[Ser6] Existence globale d'ondes planes en électromagnétisme non-linéaire, C.R.Acad.Sc. Paris, t. 304, ser.I, No 20 (1987). | Zbl | MR
,[Ser7] Systèmes hyperboliques riches de lois de conservation, Pre-publ. Lyon-St Etienne no 74 (1988), et Sém. Collège de France, “non-linear PDEs and their applications”, H. Brézis & J.-L. Lions eds., Pitman (à paraître).
,[Ser8] Les ondes planes en éléctromagnétisme non linéaire, Physica D, No 38, 227-251 (1988). | Zbl | MR
,[Ser9] Richness and the classification of quasilinear hyperbolic systems, IMA vol. in Math. and their appl. Vol 29, Springer Verlag, 1991. | Zbl | MR
,[Ser10] Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDP, Ann. Inst. Fourier, 39, 4, 953-968 (1989). | Zbl | MR | Numdam
,[Ser11] Oscillations non-linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol 8, No 34, p. 351-417, 1991. | Zbl | MR | Numdam
,[Ser12] Oscillations non-linéaires de haute fréquence ; dim=1, Pre-publ. Lyon-St Etienne no 97 (1990) et Sém. Collège de France, “non-linear PDEs and their applications”, H. Brézis & J.-L. Lions eds., Pitman (à paraître).
,[Ser13] Quelques méthodes d'étude de la propagation d'oscillations hyperboliques non-linéaires, Séminaire EDP 1990-1991, Ecole Polytechnique, exposé No XX. | Zbl | Numdam
,[Ser14] Un modèle relaxé pour les câbles inextensibles, MMAN,25,4 (1991) 465-481. | Zbl | MR | Numdam
,[Ser15] Intégrabilité d'une classe de systèmes de lois de conservation, Prépubl. ENS-Lyon No 45 (1991), à paraître dans Forum Math. | Zbl
,[Sm] Shock waves and reaction-diffusion equations, Grund. Math. Wiss. 258, Springer Verlag 1983. | Zbl | MR
,[Sp] A comprehensive introduction to differential geometry, Tome III, Publish or Perish Inc., 1975. | Zbl
,[Sto] On a difficulty in the theory of sound, Philosophical Magazine 33, 349-356, (1848).
,[Str1] The Theory of Sound, Vol. II, London : McMillan 1878.
,[Str2] Note on tidal bores, Proc. Roy. Soc. London A 81,448-449 (1908). | JFM
,[Te1] Solutions in the large for some nonlinear hyperbolic conservation laws of gas dynamics, J. Diff. Eqs. 41, 96-161 (1981). | Zbl
,[Te2] Systems of conservation laws with invariant submanifolds, Trans. Amer. Math. Soc. 280, 781-795 (1983). | Zbl | MR
,[Ts] On the Liouville Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type arising in the Bogolyubov-Whitham averaging theory, Russian Math. Surveys 39 : 6, 227-228 (1984). | Zbl | MR
,[Ts2] On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type, Soviet Math. Dokl. 31 No3, 488-491 (1985). | Zbl | MR
,[Ts3]
, , Moscow state University, 1986.[Ts4] The geometry of hamiltonian systems of hydrodynamic type. The generalized hodograph method, Math. USSR Izvsetiya 37 No2 (1991) 397-419. | Zbl | MR
,[Vo] The BV space and quasilinear equations, Math. USSR Sb. 2, 225-267 (1967). | Zbl
,[Vv] An example of non-uniqueness of a generalized solution of a quasilinear system of equations, Sov. Math. Dokl. 2, 89-90 (1961). | Zbl
,[Wa] Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J.Diff.Eqs. 68, 118-136 (1987). | Zbl | MR
,[Wh] Linear and nonlinear waves, Wiley NY 1974. | Zbl
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