POINTWISE ESTIMATES OF SOLUTIONS FOR THE MULTI-DIMENSIONAL SCALAR CONSERVATION LAWS WITH RELAXATION

被引：2
|
作者：
Deng, Shijin [1 ]
Wang, Weike [1 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 30卷 / 04期
基金：
美国国家科学基金会;
关键词：
Green's function method; pointwise estimate; multi-dimensional conservation laws with relaxation; energy estimate; NAVIER-STOKES EQUATIONS; LARGE-TIME BEHAVIOR; GREENS-FUNCTION; SPECTRAL STABILITY; HYPERBOLIC SYSTEMS; SHOCK PROFILES; GAS-DYNAMICS; SCHEMES; WAVES; CONVERGENCE;
D O I：
10.3934/dcds.2011.30.1107
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Our aim is to study the pointwise time-asymptotic behavior of solutions for the scalar conservation laws with relaxation in multi-dimensions. We construct the Green's function for the Cauchy problem of the relaxation system which satisfies the dissipative condition. Based on the estimate for the Green's function, we get the pointwise estimate for the solution. It is shown that the solution exhibits some weak Huygens principle where the characteristic 'cone' is the envelope of planes.
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页码：1107 / 1138
页数：32
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