Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $\beta (t,x)\rho u$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And the model is imposed a dissipative subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger a unique subsonic time-periodic smooth solution which is stable under small perturbations on initial data. Moreover, the time-periodic solution possesses higher regularity and stability provided a higher regular boundary condition.