Wave Structures Influenced by Effective Diffusivity in a Relaxing Gas With Quartic Nonlinearity
Abstract
ABSTRACT We analyze a quasilinear system of partial differential equations governing the unsteady one‐dimensional motion of a relaxing gas with mild dissipation. Using an asymptotic method, we derive a modified Burgers'‐type evolution equation that captures simultaneously the effects of relaxation (source term), thermo‐viscous dissipation (diffusive term), and nonconvex flux nonlinearity (quadratic–quartic terms), providing a unified evolution model for weak shock structures in relaxing gases. Numerical solutions of the associated Riemann problem reveal some novel phenomena such as sonic and double sonic shocks and Taylor's shock solution.
Fields of Study & Subjects
Navier-Stokes equation solutions
Thermoelastic and Magnetoelastic Phenomena
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Publisher
- Wiley
- Volume
- 49
- Issue
- 9
- Pages
- 9009–9021
- Publication date
- 26 January 2026
- Language
- EN