Wave Structures Influenced by Effective Diffusivity in a Relaxing Gas With Quartic Nonlinearity

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.