Wave propagation of the full compressible Oldroyd-B model

We extend the analysis of Li and Wu (2023JDE) to the full compressible Oldroyd-B model by incorporating the polymer number density $\eta$, and verify that the time-asymptotic shape of the solution contains a stationary diffusion wave superposing a moving diffusion wave with the propagation speed $\sqrt{P^{\prime}\left(\rho_{\infty}\right)+\left((K-1) L+2 \zeta \eta_{\infty}\right) \frac{\eta_{\infty}}{\rho_{\infty}}}$, where $P$ is the pressure, $\rho_{\infty}$ and $\eta_{\infty}$ are the background densities of the fluid and polymer number, the constant $L$ is the number of beads in the polymer chain and the constant $K>1$. This result implies that the polymer number density $\eta$ enhances the propagation speed of the bulk of the solution, but reduces the decay rate of the symmetric stress tensor $\mathbb{T}$ compared to the decay result of $\mathbb{T}$ in Li and Wu (2023JDE).