Generalized quasilinearization for quasilinear parabolic equations with nonlinearities of DC type

被引：5

作者：

Carl S. ^{[1
]}

Lakshmikantham V. ^{[2
]}

机构：

[1] Institut für Analysis, Fb. Mathematik und Informatik, Martin-Luther-Universitat Halle-W., Halle

[2] Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL

来源：

Journal of Optimization Theory and Applications | 2001年 / 109卷 / 01期

关键词：

d.c; functions; Generalized quasilinearization; Quadratic convergence; Quasilinear parabolic initial boundary-value problems; Upper and lower solutions;

D O I：

10.1023/A:1017505603454

中图分类号：

学科分类号：

摘要：

In this paper, we consider an initial boundary-value problem for a class of quasilinear parabolic equations whose lower-order nonlinearity is of d.c. function type with respecxt to the dependent variable. Assuming the existence of an ordered pair of weak upper and lower solutions, we establish a generalized quasilinearization method for the problem under consideration. A characteristic feature of this generalized quasilinearization method consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic.

引用

页码：27 / 50

页数：23

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