Critical conditions and comparison theorems for difference solutions of nonlinear parabolic equations

V. A. Galaktionov

Moscow

Abstract: Conditions for special pointwise estimates of difference solutions, i.e., criticality conditions, to exist, are established, and are used to prove comparison theorems for the solutions of implicit difference schemes for various non-linear parabolic equations, i.e., the conditions are found, under which one solution is majorized by another at all nodes of the space-time mesh. The results reveal that the solutions of implicit schemes display important properties of “monotonicity”, inherent in differential problems for non-linear parabolic equations.

UDC: 517.956.4:519.633

MSC: Primary 65N12; Secondary 35K60

Received: 29.04.1981

 English version: USSR Computational Mathematics and Mathematical Physics, 1983, 23:1, 74–80

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