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Existence in the large for quasilinear hyperbolic conservation laws. (English) Zbl 0268.35066


MSC:

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

[1] Lax, P. D., Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10, 537–566 (1957) · Zbl 0081.08803
[2] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697–715 (1965) · Zbl 0141.28902
[3] Glimm, J., & P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc. No. 101. 1967, 1970 · Zbl 0146.33803
[4] Nishida, T., Global solutions for an initial boundary value problem of a quasilinear hyperolic system. Proc. Japan Acad. 44, 642–646 (1968) · Zbl 0167.10301
[5] Johnson, J., & J. A. Smoller, Global solutions for an extended class of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 32, 169–189 (1969) · Zbl 0167.10204
[6] Bakhvarov, N., On the existence of regular solutions in the large for quasilinear hyperbolic systems. Zhur. Vychisl. Mat. i Mathemat. Fiz. 10, 969–980 (1970)
[7] DiPerna, R., Global solutions to a class of nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 26, 1–28 (1973) · Zbl 0256.35053
[8] Greenberg, J., The Cauchy problem for the quasilinear wave equation, private communication
[9] Nishida, T., & J. A. Smoller, Solutions in the large for some nonlinear hyperbolic conservation laws. Comm Pure Appl. Math. 26, 183–200 (1973) · Zbl 0267.35058
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