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Uniqueness and stability theorem for the generalized solution of the initial-value problem for a class of quasi-linear equations in several space variables

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References

  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).

    Google Scholar 

  2. Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 1, 159–193 (1954).

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  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.

    Google Scholar 

  7. Cesari, L., Sulle funzioni a variazione limitata. Annali Scuola Norm. Sup. Pisa, (2) 5, 299–313 (1936).

    Google Scholar 

  8. Krickeberg, K., Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nicht parametrischer Flächen. Ann. Mat. Pura Appl., (4) 44, 105–133 (1957).

    Google Scholar 

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Authors and Affiliations

  1. University of California, San Diego

    Edward Conway & Joel Smoller

  2. University of Michigan, Ann Arbor

    Edward Conway & Joel Smoller

Authors
  1. Edward Conway
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  2. Joel Smoller
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Communicated by L. Cesari

The authors acknowledge partial support under grant number NSF-GP-3465 while they were visiting members of the Courant Institute of Mathematical Sciences.

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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. Arch. Rational Mech. Anal. 23, 399–408 (1967). https://doi.org/10.1007/BF00276782

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  • DOI: https://doi.org/10.1007/BF00276782

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