A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions

被引:14
作者
Kobayasi, Kazuo [1 ]
机构
[1] Waseda Univ, Sch Educ, Dept Math, Shinjuku Ku, Tokyo 1698050, Japan
基金
日本学术振兴会;
关键词
degenerate parabolic equation; initial-boundary value problem; kinetic formulation; kinetic traces; entropy sub and supersolution; comparison theorem;
D O I
10.1016/j.jde.2006.07.008
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the comparison principle for degenerate parabolic-hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and supersolution. The L-1 contractivity and, therefore, uniqueness of entropy solutions has been obtained so far by some authors, but it seems that any comparison theorem is not proven. The method used there is the doubling variable technique due to Kruzkov. Our method is based upon the kinetic formulation and the kinetic techniques. By developing the kinetic techniques for degenerate parabolic-hyperbolic equations with boundary conditions, we can obtain a comparison property which obviously extends the. L-1 contractive property. (c) 2006 Elsevier Inc. All rights reserved.
引用
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页码:682 / 701
页数:20
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