A new variation for the relativistic Euler equations

Advances in Difference Equations

Hanan A. Alkhidhr¹  Mahmoud A. E. Abdelrahman² 

[1] Department of Mathematics, College of Science, Qassim University, Buraidah, Saudi Arabia;Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia;Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt;

关键词: Total variation;    Nonlinear waves;    Riemann solutions;    Wave interaction;    Glimm scheme;    35B40;    35L45;    35L65;    76Y05;   

DOI  :  10.1186/s13662-020-02990-6

来源: Springer

【 摘 要 】

The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

【 授权许可】

CC BY