Journal of the Mathematical Society of Japan

A generalized truncation method for multivalued parabolic problems

Livinus U. UKO

Full-text: Open access

Abstract

The generalized truncation method (formerly referred to as the proximal correction method) was recently introduced for the time-discretization of parabolic variational inequalities. The main attraction of the method --- which generalizes the truncation method developed by A. Berger for obstacle problems --- is the fact that the problems to be solved at each time step are elliptic equations rather than elliptic variational inequalities.

In this paper we apply the new method to a class of problems which includes parabolic variational inequalities as a special case. The convergence results which we obtain in this general context also give rise to new results when applied to the special case of variational inequalities.

We also discuss the applications of our results to several problems that occur in various branches of applied Mathematics.

Article information

Source
J. Math. Soc. Japan, Volume 50, Number 3 (1998), 719-735.

Dates
First available in Project Euclid: 27 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1225113729

Digital Object Identifier
doi:10.2969/jmsj/05030719

Mathematical Reviews number (MathSciNet)
MR1626358

Zentralblatt MATH identifier
0914.35070

Subjects
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40] 49J40: Variational methods including variational inequalities [See also 47J20]

Citation

UKO, Livinus U. A generalized truncation method for multivalued parabolic problems. J. Math. Soc. Japan 50 (1998), no. 3, 719--735. doi:10.2969/jmsj/05030719. https://projecteuclid.org/euclid.jmsj/1225113729


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