Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The maximum-minimum principles for a quasi-linear parabolic finite difference equation

Author: Thomas C. T. Ting
Journal: Quart. Appl. Math. 22 (1964), 47-55
DOI: https://doi.org/10.1090/qam/168136
MathSciNet review: 168136
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Abstract | References | Additional Information

Abstract: A strong maximum principle for second order parabolic equations has been introduced by L. Nirenberg. The present paper contains both strong and weak maximum-minimum principles for various finite difference equations which approximate a quasi-linear parabolic differential equation. A proof of the existence and uniqueness of the solution of the finite difference equations is also presented.

References [Enhancements On Off] (What's this?)

  • [1] T. C. T. Ting and P. S. Symonds, Longitudinal impact on visco-plastic rods--General properties, Tech. Report NSF-G17220/5, Division of Engineering, Brown University, February 1963 (to be published)
  • [2] Louis Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167–177. MR 0055544, https://doi.org/10.1002/cpa.3160060202
  • [3] I. G. Petrovsky, Lectures on partial differential equations, Interscience Publishers, New York-London, 1954. Translated by A. Shenitzer. MR 0065760
  • [4] T. C. T. Ting, Longitudinal impact on visco-plastic rods--Some analytic solutions (in preparation)
  • [5] George E. Forsythe and Wolfgang R. Wasow, Finite-difference methods for partial differential equations, Applied Mathematics Series, John Wiley & Sons, Inc., New York-London, 1960. MR 0130124
  • [6] G. Pólya and G. Szegö, Sur quelques propríetés qualitatives de la propagation de la chaleur, Comptes Rendus, 192 (1931) 1340-1342

Additional Information

DOI: https://doi.org/10.1090/qam/168136
Article copyright: © Copyright 1964 American Mathematical Society

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