Vanishing viscosity limit for Riemann solutions to a 2×2 hyperbolic system with linear damping

Article type: Research Article

Authors: De la cruz, Richard^{; *} | Juajibioy, Juan

Affiliations: School of Mathematics and Statistics, Universidad Pedagógica y Tecnológica de Colombia, Av. Central del Norte 39-115 Of. M-101, Tunja, Boyacá, 150003, Colombia. E-mails: richard.delacruz@uptc.edu.co, juan.juajibioy@uptc.edu.co

Correspondence: [*] Corresponding author. E-mail: richard.delacruz@uptc.edu.co.

Abstract: In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2×2 system of conservation laws with linear damping.

Keywords: Nonstrictly hyperbolic system, linear damping, Riemann problem, time-dependent viscous system, delta shock wave solution

DOI: 10.3233/ASY-211690

Journal: Asymptotic Analysis, vol. 127, no. 3, pp. 275-296, 2022