Archive for Rational Mechanics and Analysis

, Volume 18, Issue 1, pp 14–26 | Cite as

Maximum properties of Cauchy's problem in three-dimensional space-time

  • Duane Sather


Neural Network Complex System Nonlinear Dynamics Electromagnetism Maximum Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Agmon, S., L. Nirenberg, & M. H. Protter, A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptichyperbolic type. Comm. Pure Appl. Math. 6, 455–470 (1953).MathSciNetCrossRefGoogle Scholar
  2. [2]
    Douglis, A., The problem of Cauchy for linear, hyperbolic equations of second order. Comm. Pure Appl. Math. 7, 271–295 (1954).MathSciNetCrossRefGoogle Scholar
  3. [3]
    Germain, P., & R. Bader, Sur le problème de Tricomi. Rend. Circ. Mat. Palermo 2, 53 (1953).MathSciNetCrossRefGoogle Scholar
  4. [4]
    Protter, M. H., A maximum principle for hyperbolic equations in a neighborhood of an initial line. Trans. Amer. Math. Soc. 87, 119–129 (1958).MathSciNetCrossRefGoogle Scholar
  5. [5]
    Weinberger, H. F., A maximum property of Cauchy's problem in three-dimensional space-time. Proceedings of Symposia in Pure Mathematics, Vol. IV, Partial Differential Equations. American Mathematical Society, 1961, pp. 91–99.Google Scholar
  6. [6]
    Weinberger, H. F., A maximum property of Cauchy's problem. Ann. of Math. 64, 505–513 (1956).MathSciNetCrossRefGoogle Scholar
  7. [7]
    Weinstein, A., On a Cauchy problem with subharmonic initial values. Ann. Mat. Pura Appl. 4, 325–340 (1957).MathSciNetCrossRefGoogle Scholar
  8. [8]
    Weinstein, A., Hyperbolic and parabolic equations with subharmonic data, Symposium on the Numerical Treatment of Partial Differential Equations with Real Characteristics. Prov. Intern. Computation Centre, Rome, 1959, pp. 74–86.Google Scholar
  9. [9]
    Willmore, T. J., An Introduction to Differential Geometry. London: Oxford University Press 1959.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1965

Authors and Affiliations

  • Duane Sather
    • 1
  1. 1.Institute for Fluid Dynamics and Applied Mathematics University of MarylandCollege Park

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