On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: Global well-posedness and decay property

被引：16

作者：

Panov, Evgeny Yu. ^{[1
]}

机构：

[1] Novgorod State Univ, Bolshaya Sankt Peterburgskaya 41, Veliky Novgorod 173003, Russia

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2016年 / 13卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Conservation law; entropy solution; Besicovitch almost periodic function; decay property; Bohr compactification;

D O I：

10.1142/S0219891616500168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence and uniqueness of entropy solutions are established. We also uncover the necessary and sufficient condition for the decay of almost periodic entropy solutions as the time variable t -> + infinity. Our results are then interpreted in the framework of conservation laws on the Bohr compact.

引用

页码：633 / 659

页数：27

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