Renormalized entropy solutions to the Cauchy problem for first order quasilinear conservation laws in the class of periodic functions

2011 ◽  
Vol 177 (1) ◽  
pp. 27-49 ◽  
Author(s):  
P. V. Lysuho ◽  
E. Yu. Panov
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Entropy Solutions ◽  
Periodic Functions ◽  
First Order ◽  
The Cauchy Problem

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

2016 ◽  
Vol 13 (03) ◽  
pp. 633-659 ◽  
Author(s):  
Evgeny Yu. Panov
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Almost Periodic Functions ◽  
Entropy Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Scalar Conservation Law ◽  
The Cauchy Problem ◽  
Scalar Conservation ◽  
Necessary And Sufficient

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 [Formula: see text]. Our results are then interpreted in the framework of conservation laws on the Bohr compact.

Sign in / Sign up

Export Citation Format

Share Document