2018/04/28 by Akitaka Matsumura, Matsumura, Akitaka, Natsumi Yoshida +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1804.10841
arxiv created 2018/04/28 · openalex publication_date 2018/04/28 · arxiv updated 2018/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.