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: 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.
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)
- Louis Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167–177. MR 55544, DOI https://doi.org/10.1002/cpa.3160060202
- I. G. Petrovsky, Lectures on partial differential equations, Interscience Publishers, New York-London, 1954. Translated by A. Shenitzer. MR 0065760
T. C. T. Ting, Longitudinal impact on visco-plastic rods—Some analytic solutions (in preparation)
- 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
G. Pólya and G. Szegö, Sur quelques propríetés qualitatives de la propagation de la chaleur, Comptes Rendus, 192 (1931) 1340–1342
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)
L. Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure. Appl. Math. 6 (1953) 167–177
I. G. Petrovsky, Lectures on partial differential equations, Interscience Publishers, New York, 1954
T. C. T. Ting, Longitudinal impact on visco-plastic rods—Some analytic solutions (in preparation)
G. E. Forsythe and W. R. Wasow, Finite-difference methods for partial differential equations, Wiley, New York, 1960
G. Pólya and G. Szegö, Sur quelques propríetés qualitatives de la propagation de la chaleur, Comptes Rendus, 192 (1931) 1340–1342
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Article copyright:
© Copyright 1964
American Mathematical Society
