Global classical solutions to the Cauchy problem of conservation laws with degenerate diffusion

被引：11

作者：

Chen, Jiao ^{[1
]}

Li, Yachun ^{[2
,3
]}

Wang, Weike ^{[2
,3
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Comp Sci & Engn, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, MOE LSC, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 05期

基金：

中国国家自然科学基金; 上海市自然科学基金;

关键词：

Classical solution; Global existence; Conservation law; Degenerate diffusion; Frequency decomposition method; Green's function method; ENTROPY SOLUTIONS; PARABOLIC EQUATIONS; UNIQUENESS; STABILITY;

D O I：

10.1016/j.jde.2015.11.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the existence of the unique global classical solution with small initial data to the Cauchy problem of a scalar conservation law with degenerate diffusion by establishing the uniform a priori decay estimates of solutions. In order to compensate the degeneracy on the xi direction by the diffusion on other directions, we introduce the frequency decomposition method and obtain the low frequency estimate and the high frequency estimate of the solution by the Green's function method and energy method respectively. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：4657 / 4682

页数：26

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