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A topological degree for orbits connecting critical points of autonomous systems. (English) Zbl 0417.34053


MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A99 General theory for ordinary differential equations
54H25 Fixed-point and coincidence theorems (topological aspects)
76L05 Shock waves and blast waves in fluid mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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[1] Conley, C. C.; Smoller, J. A., Shock waves as progressive wave solutions of higher order equations, Comm. Pure Appl. Math., 23, 867-884 (1970)
[2] Conley, C. C.; Smoller, J. A., Shock waves as progressive wave solutions of higher order equations, Comm. Pure Appl. Math., 24, 459-472 (1971) · Zbl 0233.35063
[3] Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves (1948), Interscience: Interscience New York · Zbl 0041.11302
[4] Foy, L. R., Steady state solutions of hyperbolic systems of conservation laws with viscosity terms, Comm. Pure Appl. Math., 17, 177-188 (1964) · Zbl 0178.11902
[5] Friedrichs, K. O.; Lax, P. D., Systems of conservation laws with a convex extension, (Proc. Nat. Acad. Sci. USA, 68 (1971)), 1686-1688 · Zbl 0229.35061
[6] Gel’fand, I. M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Trans. Ser. 2, No. 29, 295-381 (1963) · Zbl 0127.04901
[7] Godunov, S. K., An interesting class of quasilinear systems, Dokl. Akad. Nauk SSR, 139, 521-523 (1961) · Zbl 0125.06002
[8] Godunov, S. K., No unique “blurring” of discontinuities in solutions to quasilinear systems, Dokl. Akad. Nauk SSSR, 136, 272-273 (1961) · Zbl 0117.06401
[9] Grad, H., The profile of a steady plane shock wave, Comm. Pure Appl. Math., 5, 257-300 (1952) · Zbl 0047.18801
[10] Kopell, N.; Howard, L. N., Bifurcations and trajectories and trajectories joining critical points, Advances in Math., 18, 306-358 (1975) · Zbl 0361.34026
[11] Lax, P. D., Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math., 10, 532-566 (1957) · Zbl 0081.08803
[12] Lax, P. D., Shock waves and entropy, (Zarontonello, E. H., Proceedings, Symposium at University of Wisconsin (1971)), 603-634
[13] Liu, T. P., The entropy condition and admissibility of shocks, J. Math. Anal. Appl., 53, 78-88 (1976) · Zbl 0332.76051
[14] Mock, M. S., On fourth-order dissipation and single conservation laws, Comm. Pure Appl. Math., 29, 383-388 (1976) · Zbl 0327.76031
[15] Mock, M. S., Discrete shocks and genuine nonlinearity, Michigan Math. J., 25, 131-146 (1978) · Zbl 0397.35044
[16] Mock, M. S., Systems of conservation laws of mixed type, J. Differential Equations, 37, 70-88 (1980) · Zbl 0413.34017
[17] Smoller, J. A.; Conley, C. C., Shock waves as limits of progressive wave solutions of higher order equations, II, Comm. Pure Appl. Math., 133-146 (1972) · Zbl 0225.35067
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