2012/04/17 by Yue‐Jun Peng, Yue-Jun Peng, Peng, Yue-Jun +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1204.3676
25 pages, 1 figure
arxiv created 2012/04/17 · openalex publication_date 2012/04/17 · arxiv updated 2012/04/18 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We show that in one space dimension, a linearly degenerate hyperbolic system of rich type admits exact traveling wave solutions if the initial data are Riemann type outside of a space interval. In a particular case of the system including physical models, we prove the convergence of entropy solutions to traveling waves in the L1 norm as the time goes to infinity. The traveling waves are determined explicitly in terms of the initial data and the system. We also obtain the stability of entropy solutions in L1.