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Conway, E.; Smoller, J.

Uniqueness and stability theorem for the generalized solution of the initial-value problem for a class of quasi-linear equations in several space variables. (English) Zbl 0157.16701

Arch. Ration. Mech. Anal. 23, 399-408 (1967).
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Cited in 9 Documents

Keywords:

partial differential equations
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[1] Conwway, E., & J. Smoller, Global solution of the Cauchy problem for quasi-linear first order equations in several space variables. Comm. Pure Appl. Math. 19, 95–105 (1966). · Zbl 0138.34701 · doi:10.1002/cpa.3160190107
[2] Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 1, 159–193 (1954). · Zbl 0055.19404 · doi:10.1002/cpa.3160070112
[3] Oleinik, O. A., On discontinuous solutions of non-linear differential equations. Uspekhi Mat. Nauk., 12, 3–73 (1957). English translation, Amer. Math. Soc. Trans., ser. 2, no.26, pp.95–192.
[4] Oleinik, O. A., Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation. Uspekhi Mat. Nauk. 14, 165–170 (1959). English translation Amer. Math. Soc. Trans., ser.2, no.33, pp.285–290.
[5] Rozdestvenskii, B. L., Uniqueness of the generalized solution of the Cauchy problem for hyperbolic systems of quasi-linear equations. Dokl. Akad. Nauk., SSSR, 112, 762–765 (1958). English translation, Amer. Math. Soc. Trans., ser. 2, no.42, pp.37–40.
[6] Wu Zhuo-Qun, On the existence and uniqueness of generalized solutions of the Cauchy problem for quasi-linear equations of first order without convexity conditions. Acta Math. Sinica, 13, no.4, 515–530 (1963). English translation, Amer. Math. Soc. Chinese Translation, 4, no.4, 561–577. · Zbl 0154.10805
[7] Cesari, L., Sulle funzioni a variazione limitata. Annali Scuola Norm. Sup. Pisa, (2) 5, 299–313 (1936). · Zbl 0014.29605
[8] Krickeberg, K., Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nicht parametrischer Flächen. Ann. Mat. Pura Appl., (4) 44, 105–133 (1957). · Zbl 0082.26702 · doi:10.1007/BF02415194
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