Some recent methods for partial differential equations of divergence form

被引：5
作者：
Chen, GQ [1 ]
机构：
[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA
来源：
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2003年 / 34卷 / 01期
基金：
美国国家科学基金会;
关键词：
partial differential equations; divergence form; hyperbolic conservation laws; degenerate parabolic-hyperbolic equations; mixed elliptic-hyperbolic type; entropy methods; kinetic methods; free boundary methods; divergence-measure fields; kinetic formulations; free boundary iterations; compensated compactness; test function methods;
D O I：
10.1007/s00574-003-0005-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Some recent methods for solving second-order nonlinear partial differential equations of divergence form and related nonlinear problems are surveyed. These methods include entropy methods via the theory of divergence-measure fields for hyperbolic conservation laws, kinetic methods via kinetic formulations for degenerate parabolic-hyperbolic equations, and free-boundary methods via free-boundary iterations for multidimensional transonic shocks for nonlinear equation of mixed elliptic-hyperbolic type. Some recent trends in this direction are also discussed.
引用
收藏
页码：107 / 144
页数：38
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